The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  1  X  0  1  1  X  1  1  X  0  1  X  1  1  X  1  1  1  0  X  X  1  1  1  1  1  1  1  X  1  X  1  0  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  0  X  X  0  0  X  X  X  X  0  X  X  X  X  0  0  0  X  0  0  X  X  X  0  X  0  0  0  0  X  X  X  0  X  0  0  0  X  0  X  0  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  X  0  X  X  X  X  X  X  0  X  X  0  X  X  X  0  X  0  X  X  X  X  X  X  0  0  0  0  X  X  0  X  0  0  0  0  0  X  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  0  0  X  X  X  X  X  X  0  X  0  X  X  X  0  X  X  X  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  X  0  0  X  0  X  0  0  0  0  X  0  X  0  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  0  X  X  0  X  X  X  0  0  X  X  0  X  0  X  X  0  0  X  0  X  0  X  X  0  0  X  X  X  0  0  X  X  X  0  X  0  X  X  0  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  0  0  0  X  X  0  X  X  X  0  0  0  X  X  X  0  0  X  X  0  0  0  X  0  X  0  X  X  0  0  X  0  X  X  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  X  0  X  0  0  X  0  X  0  X  0  X  0  X  0  X  0  X  X  X  0  X  X  X  0  0  X  0  X  0  X  X  0  0  X  X  0  0  X  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  X  0  X  0  X  X  X  0  X  X  0  X  X  0  0  0  X  0  X  0  X  0  X  0  X  X  0  0  0  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  X  0  0  0  0  0  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  0  X  0  X  0  0  X  X  0  X  0  0  X  X  X  X  0  0  X  X  0  X  X  X  X  0  X  0  0  0  X  X  0  X  0  0  0  X  X  X  X  X  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  X  0  X  0  X  X  X  0  X  0  X  X  X  X  0  X  0  0  0  X  0  0  X  0  0  X  0  0  0  X  X  0  X  0  0  X  0  0  X  0  0  0  X  X  X  0  0  X  0  0  X  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+55x^66+4x^67+90x^68+24x^69+101x^70+68x^71+117x^72+106x^73+87x^74+138x^75+73x^76+168x^77+81x^78+160x^79+74x^80+156x^81+61x^82+128x^83+53x^84+48x^85+44x^86+12x^87+50x^88+10x^89+45x^90+2x^91+35x^92+27x^94+13x^96+8x^98+5x^100+2x^102+1x^104+1x^118

The gray image is a linear code over GF(2) with n=156, k=11 and d=66.
This code was found by Heurico 1.16 in 79 seconds.