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  1 X^2+X  1  0  0  1 X^2+X  1  1  1  1  1  1  1  1  X X^2  1 X^2+X  1  1  1  1  1  X  1  0  1  X  0  0 X^2 X^2+X  X X^2 X^2 X^2  X  X X^2+X  0 X^2+X X^2+X X^2  X  X X^2  1  1  1  1 X^2+X  1  1 X^2+X  X X^2  1  1
 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+X+1 X^2  X  1  1 X+1  X  X X^2+X  0 X^2+1 X+1  0 X^2+1 X+1 X^2+X  1 X^2+X+1  X X^2+1 X^2+X+1 X^2+1 X^2+X  X X^2  X  1 X^2+X  0  1  X  1  1  1  0  X  X  1  1  1 X^2+X  1  1 X^2+X  1  1 X^2+X  0 X^2  0 X^2  1 X^2+X  X  1  1 X^2+X  X  X
 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  X  1 X^2+1  1  X  1  1 X^2 X+1 X^2+X  X  1 X^2+1  0 X^2+X+1  1 X+1 X^2  1  1 X^2+X X^2+X+1 X^2+1 X+1  1  X  1  0  1 X+1 X^2+X  1 X+1 X^2+X+1  1  1  0  1 X^2+1 X+1  1 X^2+X  0  1  1 X^2+1  1  0 X^2+X+1 X^2 X^2+X+1 X^2+X X^2+X+1 X^2 X^2 X+1  1  0  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  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  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+128x^78+108x^79+202x^80+120x^81+114x^82+104x^83+84x^84+8x^85+39x^86+32x^87+36x^88+1x^90+4x^92+20x^94+12x^95+9x^96+1x^102+1x^106

The gray image is a linear code over GF(2) with n=328, k=10 and d=156.
This code was found by Heurico 1.16 in 0.336 seconds.