The generator matrix

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

generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+137x^74+257x^76+48x^77+353x^78+132x^79+454x^80+192x^81+421x^82+260x^83+437x^84+240x^85+351x^86+108x^87+235x^88+32x^89+178x^90+12x^91+114x^92+68x^94+33x^96+26x^98+4x^100+2x^106+1x^128

The gray image is a linear code over GF(2) with n=332, k=12 and d=148.
This code was found by Heurico 1.16 in 2.12 seconds.