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

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+64x^78+110x^79+112x^80+124x^81+94x^82+92x^83+98x^84+128x^85+68x^86+16x^87+40x^88+4x^89+29x^90+36x^91+2x^92+1x^96+2x^111+2x^112+1x^122

The gray image is a linear code over GF(2) with n=332, k=10 and d=156.
This code was found by Heurico 1.16 in 0.462 seconds.