The generator matrix

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

generates a code of length 83 over Z2[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+43x^72+116x^73+141x^74+188x^75+240x^76+204x^77+204x^78+224x^79+225x^80+256x^81+221x^82+222x^83+235x^84+198x^85+178x^86+182x^87+174x^88+122x^89+147x^90+138x^91+77x^92+90x^93+74x^94+58x^95+53x^96+34x^97+23x^98+12x^99+8x^100+4x^101+4x^102

The gray image is a linear code over GF(2) with n=166, k=12 and d=72.
This code was found by Heurico 1.10 in 1.09 seconds.