The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+148x^75+270x^76+268x^77+232x^78+194x^79+183x^80+138x^81+117x^82+124x^83+111x^84+58x^85+48x^86+32x^87+22x^88+18x^89+7x^90+12x^91+29x^92+30x^93+3x^94+2x^95+1x^102

The gray image is a linear code over GF(2) with n=320, k=11 and d=150.
This code was found by Heurico 1.16 in 0.463 seconds.