The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 1 0 0 1 1 1 X 1 X 0 1 1 X 0 X X 1 X 0 X 1 0 1 0 1 0 0 1 1 1 1 X X 1 1 1 1 1 X 1 0 0 1 0 X X 0 1 0 1
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X X+1 X 1 1 1 0 1 X+1 X+1 0 X+1 X+1 1 1 1 X X+1 X 1 0 0 1 X X 0 1 0 1 X+1 1 0 0 X 1 0 0 1 1 X X 1 0 X+1 1 1 X+1 1 0 X X+1 0 X 0 1 X X 1 X 1 X 1 0
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 0 X X 1 0 1 0 1 X X+1 X+1 0 0 X 1 0 X X+1 1 X+1 1 X X X+1 1 1 X+1 X+1 X 1 1 0 1 0 X X 0 X X+1 X 1 0 X X 1 X+1 X X X+1 X X+1 1 X+1 0 0 0
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X X+1 0 1 X 0 X 1 X 1 X+1 X 0 X+1 X+1 1 1 0 X+1 0 X 0 X 1 0 X X+1 X 0 X+1 X+1 0 X 1 0 X+1 1 0 1 0 0 X+1 X 1 X X X 0 X+1 0 1 1 X 1 1 0 X X 1 X 1 1 X 0
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 X 1 X X+1 1 0 X+1 X+1 0 X+1 X+1 X 0 1 X X 0 1 1 X+1 0 0 1 X+1 X X 1 0 0 1 0 X X+1 0 1 X X+1 0 X X 0 X X+1 X+1 0 X+1 X+1 1 1 X X 1 X 1 X+1 0 1 1 0 0 1 X X
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X 0 X+1 X+1 0 X+1 0 1 X 0 1 X+1 X+1 X+1 X+1 0 1 1 0 1 1 0 X X 0 0 X X+1 X+1 0 X X 1 0 0 0 X X 0 0 1 1 X X+1 X+1 1 1 0 1 X+1 X+1 1 X+1 1 0 X X X X+1 0 X X X+1 0
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 X 0 0 X X X 0 0 X X X X 0 0 X X X 0 0 0 0 X 0 X X X 0 X X 0 X X 0 X 0 X X X X X X 0 X 0 0 0 X X 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+53x^66+162x^67+241x^68+276x^69+293x^70+342x^71+385x^72+428x^73+434x^74+448x^75+469x^76+444x^77+466x^78+418x^79+399x^80+430x^81+448x^82+392x^83+341x^84+310x^85+225x^86+216x^87+168x^88+138x^89+97x^90+62x^91+40x^92+18x^93+27x^94+8x^95+3x^96+4x^97+4x^98+1x^100+1x^102

The gray image is a linear code over GF(2) with n=156, k=13 and d=66.
This code was found by Heurico 1.10 in 3.84 seconds.