The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+60x^66+42x^67+135x^68+84x^69+177x^70+152x^71+167x^72+238x^73+195x^74+230x^75+249x^76+270x^77+207x^78+280x^79+205x^80+244x^81+177x^82+238x^83+132x^84+152x^85+121x^86+80x^87+82x^88+30x^89+53x^90+2x^91+21x^92+6x^93+21x^94+24x^96+11x^98+7x^100+2x^102+1x^104

The gray image is a linear code over GF(2) with n=156, k=12 and d=66.
This code was found by Heurico 1.16 in 72 seconds.