The generator matrix

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

generates a code of length 82 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+142x^78+96x^79+219x^80+88x^81+179x^82+12x^83+92x^84+16x^85+52x^86+12x^87+28x^88+24x^89+37x^90+4x^91+8x^92+4x^94+4x^95+1x^96+2x^98+2x^100+1x^104

The gray image is a linear code over GF(2) with n=328, k=10 and d=156.
This code was found by Heurico 1.11 in 0.25 seconds.