The generator matrix

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

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+250x^78+108x^79+351x^80+120x^81+296x^82+104x^83+231x^84+104x^85+168x^86+28x^87+90x^88+28x^89+56x^90+16x^91+28x^92+22x^94+28x^96+4x^97+8x^98+5x^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 1.16 in 0.568 seconds.