The generator matrix

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

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+288x^76+520x^78+715x^80+562x^82+685x^84+534x^86+501x^88+162x^90+72x^92+10x^94+22x^96+4x^98+16x^100+1x^104+2x^108+1x^116

The gray image is a linear code over GF(2) with n=332, k=12 and d=152.
This code was found by Heurico 1.16 in 46.2 seconds.