The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  1  X  1  X  1  0  1  X  0  1  X  X  1  X  1  1  X  1  1  1  0  X  X  0  1  X  X  1  1  1  1  X  0  0  0  0  0  0  X  0  1  1  1  0  0  1  1  X  X  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  X  1 X+1  1  1  1 X+1  1 X+1  X  1  X  1  1 X+1  1  0 X+1  X  1  0  X  X  1  1  X  1  1  0  1  0  X  X  0  1  X  1  X  0  X  0  1  X  X  X  1  0  1  X  1  1  1  X  X
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  0  0  X X+1 X+1 X+1 X+1  0  1  X X+1  0  1 X+1 X+1 X+1  X  1  1 X+1  X  1  0  1  X X+1  0  X  X  1  1  X  0 X+1  1 X+1  1  1  X  X  1  X  0 X+1 X+1  X X+1  0  0 X+1  0  1 X+1
 0  0  0  1  0  0  X  1 X+1  1  0  1  1  0 X+1  1  X X+1  0 X+1  1  1  0  X  1  0 X+1  0 X+1  0  X  1  X  0  X  X  1  1  1 X+1  X  1 X+1  X  X  X  0  1 X+1 X+1 X+1  1  0  0  0  1 X+1  0  0 X+1 X+1  1  X  X  1  X
 0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  X  1  1  0  X  1  1  0  0  1 X+1  X  1  X  0  X X+1  1  1 X+1  X  0  1 X+1  1  1 X+1  1  X  0  X X+1  1  0 X+1 X+1  X  X X+1  1  X  1  X  X X+1  1  X  0 X+1 X+1  X  X  X
 0  0  0  0  0  1  1  X  1  1 X+1  X  1  1 X+1  0  0  0  1  1  X X+1 X+1  X X+1  X X+1  1  X  0  1  X  X X+1 X+1  X  0  0 X+1  1 X+1  1 X+1  0 X+1  1  X  1  1  1  0 X+1  1  0  0  0  X X+1  0 X+1  1  1  X X+1  1  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+55x^56+144x^57+166x^58+186x^59+228x^60+266x^61+253x^62+242x^63+238x^64+242x^65+235x^66+206x^67+225x^68+258x^69+208x^70+144x^71+194x^72+182x^73+119x^74+86x^75+79x^76+52x^77+36x^78+22x^79+4x^80+8x^81+4x^82+10x^83+3x^86

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 2.22 seconds.