The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+108x^72+100x^73+212x^74+248x^75+262x^76+320x^77+312x^78+328x^79+356x^80+408x^81+240x^82+328x^83+303x^84+192x^85+104x^86+120x^87+85x^88+4x^89+28x^90+17x^92+6x^96+9x^100+3x^104+1x^108+1x^112

The gray image is a linear code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 1.47 seconds.