The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 X X 0 1 X 1 1 0 1 1 1 1 0 1 X 0 1 1 0 X 1 0 X 0 1 1 1 0 X X 1 1 1 1 1 1 1 X 1 1 0 0 1 1 1 1 1 0 1
0 1 0 0 1 1 1 0 0 1 X+1 X 1 1 X 0 0 1 X+1 1 1 1 X+1 1 X 0 X X+1 0 X 0 1 1 X 1 0 1 1 0 1 1 1 1 X 1 X+1 X X 1 0 X+1 0 1 X+1 0 X 1 X 0 1 0 0 X 1 1 X 0 X+1
0 0 1 1 1 0 1 0 1 X+1 0 X 0 X+1 1 X+1 1 1 0 X 1 X+1 0 X X+1 X 1 X+1 X+1 1 1 1 1 1 X+1 X+1 0 1 1 0 X+1 X+1 X 0 X+1 0 1 1 X X 0 X 0 X+1 X+1 1 X+1 0 1 1 1 0 0 X+1 1 1 1 0
0 0 0 X 0 0 0 0 0 X X X X X 0 0 0 0 0 0 X X X 0 0 0 X 0 0 X 0 0 X X X 0 X X X 0 X 0 X 0 0 0 X 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 X X 0 X
0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 X X X X X X X 0 X 0 0 X X X X 0 0 0 X X 0 0 0 X X X 0 X 0 0 X X X X 0 0 0 0 0 X X X 0 0 X 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 X X X X X 0 0 X X X X X X 0 0 0 X 0 X X 0 X 0 X 0 X 0 0 X X X X 0 X 0 0 0 X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X X X X X 0 0 0 X X 0 X 0 0 0 X X 0 X 0 X X 0 X X 0 X X X 0 X X 0 0 X X 0 0 0 X 0 0 0 0 0 0 0 X
0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 X X 0 X 0 X X X X 0 0 0 X 0 0 X 0 X X 0 0 0 0 X X 0 X 0 X 0 0 0 0 X X 0 0 X 0 X 0 X 0 X 0 X 0 0 0 0
0 0 0 0 0 0 0 0 X X X X X X 0 X 0 0 0 0 X X X 0 X 0 X 0 X 0 X 0 0 0 0 X 0 X 0 0 0 X 0 X X X X X 0 X 0 0 0 0 X 0 0 X 0 X 0 0 X 0 0 X X X
generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 57.
Homogenous weight enumerator: w(x)=1x^0+34x^57+101x^58+110x^59+173x^60+168x^61+192x^62+208x^63+211x^64+230x^65+263x^66+290x^67+257x^68+254x^69+234x^70+252x^71+208x^72+226x^73+147x^74+126x^75+115x^76+88x^77+56x^78+36x^79+40x^80+22x^81+13x^82+2x^83+15x^84+2x^85+14x^86+4x^88+4x^90
The gray image is a linear code over GF(2) with n=136, k=12 and d=57.
This code was found by Heurico 1.16 in 3.11 seconds.