The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 1 1 0 0 1 0 0 1 0 1 1 1 X X 1 1 1 X 1 0 0 X 0 X X 1 1 X 1 1 X 1 1 X 1 0 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 1 1 0 0 1 X+1 1 X 1 1 X 0 X 1 1 X+1 X+1 X+1 0 X 0 0 0 1 X 1 1 X 1 0 1 X 1 1 0 1 1 X+1
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 1 X 0 X+1 1 X 1 X X X 1 X+1 0 X 1 X 1 X+1 X+1 1 1 1 1 1 X+1 1 X 0 1 X+1 X+1 0 1 1 X 1 X+1 X 1
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 1 X X+1 1 X+1 1 1 X+1 1 0 1 1 X X 0 X X X+1 X+1 0 1 X X+1 0 0 0 0 X+1 X+1 1 X+1 0 X+1 1 1 1 0 X+1 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X 1 X X 1 X X+1 1 X 1 X X+1 X X+1 1 0 0 X+1 0 X 1 X X+1 X+1 X+1 1 0 1 X X 0 1 1 1 0 X+1 1 1 X+1
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 0 1 0 0 X+1 0 X+1 X+1 1 X+1 1 X X+1 0 1 X+1 X 1 0 X+1 X X+1 X 1 0 X X X+1 X+1 X X 0 1 1 X 1 X 1 X+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+72x^57+134x^58+182x^59+195x^60+196x^61+249x^62+236x^63+264x^64+268x^65+223x^66+256x^67+227x^68+186x^69+210x^70+238x^71+209x^72+138x^73+155x^74+130x^75+100x^76+90x^77+40x^78+36x^79+26x^80+10x^81+12x^82+8x^83+2x^84+1x^86+2x^87

The gray image is a linear code over GF(2) with n=134, k=12 and d=57.
This code was found by Heurico 1.10 in 0.844 seconds.