The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+40x^66+22x^67+88x^68+90x^69+147x^70+108x^71+151x^72+194x^73+176x^74+206x^75+223x^76+268x^77+240x^78+280x^79+249x^80+260x^81+179x^82+226x^83+176x^84+146x^85+135x^86+156x^87+74x^88+58x^89+54x^90+26x^91+33x^92+8x^93+34x^94+20x^96+15x^98+6x^100+4x^102+1x^104+2x^108

The gray image is a linear code over GF(2) with n=158, k=12 and d=66.
This code was found by Heurico 1.16 in 4.02 seconds.