The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+235x^74+296x^75+503x^76+276x^77+461x^78+304x^79+433x^80+264x^81+339x^82+148x^83+211x^84+90x^85+180x^86+68x^87+112x^88+40x^89+60x^90+28x^91+20x^92+14x^93+1x^94+4x^95+4x^97+4x^98

The gray image is a linear code over GF(2) with n=320, k=12 and d=148.
This code was found by Heurico 1.16 in 0.956 seconds.