The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+110x^73+219x^74+328x^75+351x^76+354x^77+372x^78+256x^79+272x^80+338x^81+350x^82+246x^83+234x^84+258x^85+172x^86+106x^87+31x^88+12x^89+16x^90+18x^91+2x^92+12x^93+19x^94+6x^95+4x^96+4x^97+2x^98+1x^100+1x^102+1x^114

The gray image is a linear code over GF(2) with n=320, k=12 and d=146.
This code was found by Heurico 1.16 in 13.2 seconds.