The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+120x^76+132x^77+192x^78+96x^79+154x^80+88x^81+68x^82+36x^83+32x^84+8x^85+16x^86+4x^87+25x^88+4x^89+12x^90+8x^91+10x^92+8x^93+8x^94+2x^96

The gray image is a linear code over GF(2) with n=320, k=10 and d=152.
This code was found by Heurico 1.16 in 0.309 seconds.