The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X
 0  X  0 X^2+X  0 X^2+X  0  X  0 X^2+X X^2+X  0  X  0  0  X  0 X^2+X  0  X  0 X^2+X  0  X  0 X^2+X  0  X  0 X^2+X X^2 X^2+X  0 X^2+X X^2  X  0 X^2+X X^2  X  0 X^2+X X^2 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X X^2 X^2+X  0  X X^2  X  0 X^2+X X^2  X  0 X^2+X X^2  X X^2 X^2+X X^2  X  X X^2 X^2 X^2+X X^2 X^2+X X^2+X  X  0 X^2 X^2  X X^2  X X^2 X^2 X^2+X  X  0  X X^2+X X^2  0  0 X^2  X X^2 X^2+X X^2+X
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+127x^92+64x^95+183x^96+384x^97+64x^99+144x^100+56x^104+1x^188

The gray image is a linear code over GF(2) with n=388, k=10 and d=184.
This code was found by Heurico 1.16 in 4.05 seconds.