The generator matrix

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

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+59x^72+130x^73+193x^74+268x^75+322x^76+298x^77+347x^78+340x^79+314x^80+362x^81+291x^82+296x^83+262x^84+210x^85+156x^86+106x^87+56x^88+16x^89+15x^90+10x^91+3x^92+4x^93+11x^94+2x^95+6x^96+4x^97+8x^98+2x^99+1x^100+1x^102+1x^106+1x^110

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 1.44 seconds.