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

generates a code of length 77 over Z2[X]/(X^3) who�s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+53x^74+112x^76+34x^78+12x^80+41x^82+1x^88+2x^108

The gray image is a linear code over GF(2) with n=308, k=8 and d=148.
This code was found by Heurico 1.16 in 0.298 seconds.