The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+544x^76+1068x^78+1547x^80+1324x^82+1140x^84+892x^86+797x^88+456x^90+288x^92+96x^94+28x^96+4x^98+4x^100+3x^104

The gray image is a linear code over GF(2) with n=332, k=13 and d=152.
This code was found by Heurico 1.11 in 185 seconds.