The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+28x^76+184x^77+44x^78+96x^79+60x^80+256x^81+80x^82+64x^83+24x^84+120x^85+4x^86+32x^87+7x^88+16x^89+2x^92+1x^100+4x^108+1x^124

The gray image is a linear code over GF(2) with n=324, k=10 and d=152.
This code was found by Heurico 1.16 in 0.425 seconds.