The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+239x^60+136x^62+331x^64+246x^66+330x^68+174x^70+210x^72+122x^74+110x^76+66x^78+38x^80+24x^82+16x^84+4x^88+1x^92

The gray image is a linear code over GF(2) with n=136, k=11 and d=60.
This code was found by Heurico 1.16 in 76.8 seconds.