The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+118x^76+120x^77+208x^78+184x^79+298x^80+128x^81+228x^82+116x^83+152x^84+84x^85+112x^86+56x^87+66x^88+48x^89+34x^90+28x^91+32x^92+4x^93+6x^94+14x^96+2x^98+6x^100+2x^102+1x^112

The gray image is a linear code over GF(2) with n=328, k=11 and d=152.
This code was found by Heurico 1.16 in 0.644 seconds.