The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+62x^77+115x^78+84x^79+162x^80+88x^81+118x^82+62x^83+118x^84+48x^85+72x^86+12x^87+30x^88+20x^89+12x^90+8x^92+6x^93+1x^102+2x^107+2x^110+1x^120

The gray image is a linear code over GF(2) with n=328, k=10 and d=154.
This code was found by Heurico 1.16 in 0.443 seconds.