The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  1  X X^2+X  1  1 X^2+X  1  1  0 X^2+X  1  1 X^2  1  1 X^2  1  X  0  1  1  1  1  1  X  1  0 X^2  1  1  1  1  1  1  1 X^2+X  1  X  1  1  1  1 X^2  1  0  X  1  X X^2  1 X^2+X  1  X  1  0  0  X  1  X  1  1 X^2+X  X  1  0  1 X^2  0  0 X^2  1 X^2  1
 0  1  0  0  1 X^2+1  1  X  1  1 X^2+X  1 X^2 X^2+X+1  0 X^2+X X^2+1 X+1  1  1 X^2 X+1 X^2+X X+1 X^2+X  1 X^2+X  1 X^2+X  1  X X^2+X  1 X^2+X+1  1 X^2+1  1  1  X X^2 X^2  1  1 X^2+X+1  0  1  X  1 X^2+X X^2+X X^2+1 X+1  1 X^2+1  1  1 X^2  1  0 X^2+1  1 X+1  1  X  1  1 X^2+X X^2+X+1  1  X X^2+X+1  1 X^2  1  1  X X^2  1 X^2+X  1  X  X  1
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X  1 X^2 X^2+1  1 X^2  1  1  X X+1 X^2+1 X^2 X^2+X  1  1  X X^2+X+1  1  0  0  1 X^2 X^2+1  X X^2+X+1  0 X+1  1  X X^2+X+1 X^2+1  X X+1  1 X^2+X X+1 X^2  1 X^2+1  X X^2+X X+1  0 X^2 X^2 X^2+X+1 X^2+1  0  X  1  1  X X^2+X+1  1  X X^2+X X+1 X+1  1 X^2+X+1 X^2+X+1 X^2+X+1 X^2+1 X^2+1  1 X^2+1 X^2 X^2+X+1  1  1  1  X  X  1 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 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+286x^78+509x^80+400x^82+332x^84+180x^86+156x^88+60x^90+58x^92+22x^94+30x^96+12x^98+2x^100

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 0.516 seconds.