The generator matrix
1 0 0 0 1 1 1 1 0 1 X 1 X 1 X X X 0 1 X 1 1 1 X X 1 X X 1 1 1 X 1 X X 1 0 0 1 1 X X X X 1 0 1 0 1 1 1 X 0 1 1 0 1 1 1 0 1 X 1 1 1 X 1
0 1 0 0 0 1 1 X 1 X+1 1 1 1 X 0 1 0 1 0 1 X+1 1 X 1 X 0 X 1 1 X 1 0 X 1 0 0 1 1 1 X 1 1 1 X 1 1 X+1 1 X X 1 1 X 0 1 1 0 0 0 X 1 0 0 X 0 1 0
0 0 1 0 1 1 0 0 X+1 0 X X+1 1 1 1 X 1 1 0 0 X+1 1 1 1 1 X X 0 1 X+1 0 X X+1 0 X 0 X 1 X+1 1 X+1 X+1 1 1 1 0 X X+1 X+1 X X+1 X+1 X X+1 0 0 1 X+1 X X X X 1 1 0 X+1 0
0 0 0 1 1 0 1 1 1 X 1 X+1 0 X 1 X+1 X 1 X+1 0 X X+1 0 X 1 0 1 X+1 1 1 X+1 1 X X+1 1 0 0 X X+1 1 1 1 X 1 X+1 1 X+1 1 0 X+1 0 1 1 X 0 X+1 0 X 1 1 1 1 X+1 1 0 X X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X 0 X X X X X X X X X X X 0 0 X X X X X X X X X 0 0 X 0 X X X 0 0 0 X X 0 X 0 0 X X
0 0 0 0 0 X 0 0 X X X X 0 0 X 0 X 0 0 X X X 0 X 0 X X 0 X X X 0 0 0 X X 0 X 0 X X 0 0 X X 0 X 0 0 0 0 X X X 0 X X 0 X 0 0 0 X 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X X 0 0 X X X X X X 0 X X X X 0 0 0 0 0 X X X 0 X 0 0 0 X X 0 X X X X 0 0 X 0 0 0 0 0 X 0 X X X X X 0 X X 0 0
generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.
Homogenous weight enumerator: w(x)=1x^0+53x^58+86x^59+92x^60+122x^61+144x^62+148x^63+122x^64+162x^65+119x^66+108x^67+150x^68+114x^69+104x^70+80x^71+70x^72+64x^73+67x^74+62x^75+48x^76+34x^77+24x^78+28x^79+23x^80+14x^81+1x^82+6x^84+2x^85
The gray image is a linear code over GF(2) with n=134, k=11 and d=58.
This code was found by Heurico 1.16 in 0.633 seconds.