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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+50x^71+150x^72+128x^73+154x^74+218x^75+305x^76+300x^77+288x^78+394x^79+344x^80+378x^81+298x^82+214x^83+203x^84+154x^85+114x^86+96x^87+100x^88+46x^89+35x^90+40x^91+41x^92+18x^93+6x^94+12x^95+5x^96+3x^100+1x^122

The gray image is a linear code over GF(2) with n=320, k=12 and d=142.
This code was found by Heurico 1.16 in 3.39 seconds.