The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+198x^78+184x^79+344x^80+192x^81+224x^82+124x^83+187x^84+92x^85+126x^86+80x^87+81x^88+20x^89+52x^90+28x^91+31x^92+32x^93+20x^94+12x^95+8x^96+4x^98+4x^99+2x^100+2x^104

The gray image is a linear code over GF(2) with n=332, k=11 and d=156.
This code was found by Heurico 1.11 in 0.329 seconds.