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

generates a code of length 46 over Z2[X]/(X^3) who�s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+47x^40+112x^42+64x^43+116x^44+128x^45+172x^46+64x^47+158x^48+72x^50+52x^52+28x^54+9x^56+1x^80

The gray image is a linear code over GF(2) with n=184, k=10 and d=80.
This code was found by Heurico 1.16 in 0.093 seconds.