The generator matrix

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

generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+68x^56+120x^57+156x^58+194x^59+237x^60+248x^61+250x^62+262x^63+239x^64+280x^65+231x^66+228x^67+227x^68+196x^69+203x^70+198x^71+165x^72+128x^73+133x^74+104x^75+72x^76+44x^77+47x^78+36x^79+11x^80+8x^81+4x^82+2x^83+4x^84

The gray image is a linear code over GF(2) with n=132, k=12 and d=56.
This code was found by Heurico 1.16 in 2.41 seconds.