The generator matrix

1 0 0 0 0 0 1 1 1 0 1 1 X 1 X 1 X 0 X 1 1 X X 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 X 1 X X 0 X 1 1 0 0 1 0 1 1 1 0 X 1 1 X 1 0 1 X 0 1 1 0 1 1 X 1 X X 0 X 0 1 X 0 X 1
0 1 0 0 0 0 0 0 0 X 0 0 X 0 X X 1 1 1 1 1 1 1 1 1 1 X+1 X X+1 1 X+1 X+1 0 X+1 1 0 0 X X 1 0 1 X 1 0 X X X 1 1 X+1 1 X+1 1 X+1 1 0 X+1 1 1 X+1 0 1 1 X X X 0 X X+1 1 X X 1 X 1 0 0 0 0 0 X+1
0 0 1 0 0 0 0 0 X 0 0 0 0 X X X 0 0 0 X 0 X 0 X X 0 0 X X X X X X 1 1 1 1 1 X+1 X+1 1 X+1 1 1 1 1 X+1 X+1 1 1 1 X 1 X+1 X+1 0 1 0 X 0 X+1 1 X+1 X+1 1 0 1 1 X+1 1 1 X+1 1 0 0 X 0 1 X 1 X X+1
0 0 0 1 0 0 0 1 1 1 X X+1 1 0 X 1 X 1 0 X X+1 0 1 X+1 0 1 1 1 1 X X+1 0 1 1 X X+1 1 0 X+1 X X+1 X 1 0 X+1 X X+1 0 X+1 X+1 X 0 0 X+1 X+1 0 X+1 X+1 1 X+1 0 0 1 X 1 1 0 1 X+1 1 1 1 0 X 0 1 X 1 0 X 1 X
0 0 0 0 1 0 1 X X+1 1 1 X+1 X+1 0 1 X 1 1 X+1 X X X X X+1 1 0 X+1 0 0 0 1 X+1 X+1 1 X+1 0 X+1 1 X X+1 X 0 0 0 X+1 1 1 X 0 1 X 1 1 X+1 0 X 1 0 1 0 1 1 X 1 X 0 X 1 0 X+1 X+1 X+1 1 0 0 X 1 X+1 1 1 X+1 X
0 0 0 0 0 1 X 0 0 0 1 X+1 1 1 1 X+1 0 X X+1 0 0 1 X X+1 X X+1 X X+1 1 X+1 1 X+1 X X+1 0 X X+1 X X+1 X+1 1 1 X 0 0 X+1 1 1 X 1 X 0 X 1 1 X+1 0 X 0 1 X 1 0 X+1 0 0 X 0 X+1 X+1 0 0 X X 1 X X 1 0 X 1 X+1

generates a code of length 82 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+193x^72+352x^74+488x^76+488x^78+458x^80+434x^82+405x^84+354x^86+288x^88+234x^90+175x^92+122x^94+60x^96+30x^98+12x^100+2x^106

The gray image is a linear code over GF(2) with n=164, k=12 and d=72.
This code was found by Heurico 1.10 in 1.13 seconds.