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 X^2 X^2  1  1  1  1  X  1
 0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2 X^2+X X^2 X^2+X  X X^2 X^2+X X^2  0 X^2+X X^2 X^2+X X^2 X^2  0 X^2 X^2+X X^2+X X^2+X  X  0 X^2  0  0  X  X  X X^2+X  X  X  0 X^2  X X^2+X X^2 X^2
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2 X^2 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  0 X^2 X^2+X  0  X  0  X  0 X^2+X  X  0 X^2 X^2+X X^2 X^2  X X^2 X^2+X X^2  X  X  0  0 X^2+X X^2+X  X X^2+X  0 X^2  0  0  X X^2+X  X  X  0 X^2  0 X^2 X^2 X^2  X X^2  X X^2
 0  0  0  X  X  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2 X^2  X X^2+X  0 X^2  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2 X^2 X^2+X X^2+X  0  0  0  0 X^2+X  X X^2 X^2+X  0 X^2 X^2  X  X X^2+X  X X^2  0 X^2+X X^2  0  X X^2+X X^2  X  X  0 X^2  X X^2+X X^2  0  X  X  0  0 X^2+X  X X^2 X^2+X  X X^2 X^2+X X^2  X X^2  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+13x^76+44x^77+53x^78+90x^79+127x^80+80x^81+47x^82+36x^83+9x^84+4x^85+3x^86+2x^87+2x^88+1x^154

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 0.278 seconds.