The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+65x^58+128x^59+186x^60+216x^61+223x^62+232x^63+229x^64+258x^65+238x^66+264x^67+228x^68+228x^69+209x^70+184x^71+225x^72+210x^73+200x^74+136x^75+112x^76+84x^77+71x^78+64x^79+38x^80+26x^81+16x^82+16x^83+2x^84+1x^86+3x^88+2x^89+1x^90

The gray image is a linear code over GF(2) with n=136, k=12 and d=58.
This code was found by Heurico 1.16 in 2.49 seconds.