The generator matrix
1 0 0 1 1 1 0 1 1 1 1 0 X 1 0 1 0 1 1 X 0 1 1 1 0 0 X 1 X 1 1 1 1 X X 1 1 1 0 1 1 X 1 1 X 0 0 0 1 X 0 1 0 X X X X 1 1 1 X 0 0 X 1 1 1 1 X 1 1 1 1 0 1 0 1 1
0 1 0 1 0 1 1 0 0 1 X+1 1 1 X 0 X 0 X+1 X+1 1 1 1 X 1 1 0 1 1 1 X+1 0 X+1 X+1 1 X X+1 X X+1 0 0 X 1 X 1 1 1 1 0 0 0 1 X+1 1 1 1 0 1 X+1 1 X 1 0 0 1 0 X 1 1 1 1 X X 1 1 1 1 0 0
0 0 1 1 1 0 1 0 1 X+1 X X 1 0 1 1 1 X+1 0 1 0 X+1 X+1 1 X 1 X+1 X 0 X+1 0 X+1 X X+1 1 X+1 X+1 X 1 X+1 X+1 1 0 X 1 0 X 1 1 1 X 0 0 0 0 1 X+1 X+1 0 X+1 X 1 1 X 0 0 X X+1 1 0 0 X X+1 1 0 0 X 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X X 0 0 0 X X 0 X 0 0 0 X 0 X X X X X X 0 X X 0 0 X 0 0 X X 0 0 X X 0 X X X 0 X 0 0 0 X X 0 0 X 0 X 0 0 X X 0
0 0 0 0 X 0 0 0 0 0 0 X X X X 0 0 X 0 X X X X 0 0 X 0 0 X X 0 X 0 X 0 0 0 X 0 0 0 X X X 0 0 X 0 X X X 0 0 X 0 X X 0 X X 0 0 0 0 0 X X X 0 0 0 0 0 X X X X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X 0 X X 0 X 0 X X 0 X 0 X X X X X 0 0 X X X X X X 0 X X X 0 X X 0 0 0 0 0 0 0 0 X X 0 X 0 X 0 X X X 0 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X X 0 0 X X 0 X 0 0 X X 0 X X 0 0 X 0 X X X X 0 X X X 0 0 0 X 0 0 X 0 X 0 0 0 X X X X X X X 0 X X 0 0 X X 0 X 0 X 0
0 0 0 0 0 0 0 X 0 X X 0 0 0 X X X X X 0 0 0 X X 0 0 X X 0 0 0 0 X X 0 X X X X X X X X 0 X 0 X X X 0 X 0 X 0 X 0 X X 0 X 0 X X X X X X 0 X 0 X X 0 X 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 0 X 0 0 0 0 0 X 0 X 0 X X X X X X X 0 X 0 0 0 X 0 0 X 0 0 0 0 X X X 0 0 X 0 X X X X 0 X 0 0 0 X 0 X X X X X 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+18x^66+42x^67+115x^68+136x^69+179x^70+200x^71+212x^72+192x^73+208x^74+238x^75+237x^76+250x^77+234x^78+216x^79+188x^80+248x^81+197x^82+184x^83+145x^84+132x^85+111x^86+112x^87+84x^88+56x^89+54x^90+30x^91+31x^92+10x^93+16x^94+11x^96+3x^98+2x^99+4x^102
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 3.38 seconds.