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

generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+66x^57+120x^58+168x^59+212x^60+214x^61+236x^62+282x^63+262x^64+246x^65+232x^66+236x^67+246x^68+204x^69+204x^70+176x^71+216x^72+182x^73+142x^74+116x^75+83x^76+94x^77+52x^78+38x^79+32x^80+18x^81+6x^82+8x^83+3x^84+1x^88

The gray image is a linear code over GF(2) with n=134, k=12 and d=57.
This code was found by Heurico 1.16 in 2.32 seconds.