The generator matrix

 1  0  1  1  1 X^2  1  1  X  1  1 X^2+X  1  1  X  1  1 X^2 X^2+X  1  1  1  1  0  X  X  X X^2  0  1  1  1  1  0  1  1  0 X^2+X  1  1 X^2+X X^2  0  1  1  0  1  1  1  1  1 X^2 X^2+X  1  X  0 X^2  X  0 X^2+X X^2+X  X  X X^2  1  X  X  0  0  1  1  1  1 X^2  1  1  0  1  1  1  1  1  1
 0  1  1  0 X+1  1 X^2+X+1  0  1 X^2  1  1  X X^2+1  1  X X+1  1  1 X^2+X X+1  X  1  1  1  1  1  1  1  0 X^2+1 X^2 X+1  1 X^2+X X^2+1  1  1  1 X^2  1  1  0  X X+1  1 X^2+X+1  0 X^2+1 X^2+X X^2+X  X  1 X^2+X+1  1  1  1  1  1  1  1 X^2  1  1 X^2 X^2+X  1  1  X  0  1  1  0  1 X^2  1  0 X^2+X  1  0 X^2+X+1 X^2+X+1  0
 0  0  X  0  0  0  0  X X^2+X  X  X  X X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X X^2 X^2 X^2 X^2+X  0 X^2  X X^2+X  0  0 X^2+X X^2+X X^2+X  X  X X^2+X X^2  0  0  0  X X^2  X X^2 X^2+X X^2 X^2+X  X X^2 X^2  X  0 X^2+X X^2+X X^2 X^2+X  0 X^2  0 X^2+X X^2+X  X  0 X^2  X X^2  0  0  0  0  0 X^2+X  X X^2 X^2+X  X  0 X^2+X X^2+X X^2+X  X  0
 0  0  0  X X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  X  0  0  0 X^2+X  X X^2+X X^2+X X^2+X X^2 X^2  X X^2  X  X  0  0 X^2 X^2  0  0 X^2+X X^2+X X^2+X  0  X  X X^2+X  X X^2 X^2+X  X X^2 X^2  0  X  X  X X^2+X  0  X  X X^2 X^2+X X^2+X X^2 X^2  0 X^2+X  X  0  X  0  0 X^2 X^2+X X^2  X X^2+X  X X^2 X^2 X^2 X^2+X X^2+X  X X^2+X  X  0 X^2+X  X  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+57x^78+116x^79+126x^80+112x^81+95x^82+116x^83+111x^84+76x^85+49x^86+40x^87+39x^88+36x^89+17x^90+10x^91+8x^92+1x^94+4x^95+2x^99+2x^104+4x^106+1x^108+1x^110

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 0.361 seconds.