The generator matrix
1 0 0 0 1 1 1 X 0 0 0 1 1 1 1 0 X 1 1 1 0 1 0 X X 1 0 1 1 0 X 1 X 1 1 1 1 X 0 0 X 1 X 1 1 0 X 0 X 1 0 0 0 1 1 1 0 1 0 X X 0 1 X 1 X 1 1
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 1 1 X 1 X 0 0 1 1 X+1 0 0 X+1 1 X 0 1 X+1 0 X X 1 0 X 1 X X X X+1 1 0 1 X 1 0 1 1 X X+1 1 X X+1 1 1 1 1 X+1 1 X+1 0 X+1 1
0 0 1 0 0 1 1 1 X 1 X+1 1 1 X 0 0 X 0 X+1 X+1 1 0 1 1 0 1 1 1 X+1 1 1 X 0 X 0 1 X+1 1 X 1 X 0 X 1 X+1 1 1 X+1 1 X 1 X X+1 X 1 X+1 0 X+1 0 1 1 0 X 1 1 X X+1 1
0 0 0 1 1 1 0 1 1 X+1 X 0 1 X+1 X 1 1 1 X 0 X 0 X+1 X X 1 X X+1 X 1 1 X+1 X+1 0 X X X X 1 0 0 X 1 X+1 X+1 1 1 X+1 0 X 0 0 X+1 X+1 X+1 1 1 X+1 X+1 1 1 0 1 1 0 1 1 0
0 0 0 0 X 0 0 0 0 0 0 X X X X X X 0 0 0 X X X 0 X X 0 X X 0 X X 0 X 0 0 0 X X X 0 X 0 X X X 0 X X 0 X 0 0 X 0 X X 0 0 X 0 0 0 X X 0 X 0
0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 X X X X X X X X X X X 0 X X X X 0 X X 0 X X X X 0 0 X X 0 0 X 0 X X 0 0 X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X 0 X X 0 X X X 0 X 0 X 0 0 X 0 X X X X X X X 0 X X 0 X X 0 X 0 X 0 X X 0 0 X 0 0 X
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+187x^60+212x^62+329x^64+294x^66+261x^68+166x^70+172x^72+136x^74+133x^76+68x^78+58x^80+18x^82+11x^84+2x^86
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 0.803 seconds.