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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+56x^76+146x^78+132x^80+100x^82+60x^84+10x^86+6x^88+1x^128

The gray image is a linear code over GF(2) with n=320, k=9 and d=152.
This code was found by Heurico 1.16 in 0.365 seconds.