The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 X 0 1 1 1 X 1 0 1 1 X 0 0 1 1 1 0 1 X 1 X X 1 0 1 0 1 1 1 1 1 1 X 0 X X 1 X 1 1 X X 1 1 0 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X+1 1 1 1 X 1 0 0 1 X X 1 1 1 0 1 1 X 1 0 1 1 1 X+1 1 X+1 1 0 X X+1 X X X 1 0 1 1 1 1 0 X 1 1 1 0 1 X+1 1 X
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 0 1 0 1 1 X+1 1 X+1 X 1 0 1 0 0 X X+1 1 1 X+1 1 X X 1 X 0 0 1 1 0 0 1 X+1 0 1 1 1 X X X+1 1 1 X 0 X+1 0 0 X+1 1 1
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X 0 0 0 X X X X X 0 X X 0 0 X X 0 X 0 X 0 0 X X X X X 0 X 0 X X X X 0 0 X X X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 X X X X 0 0 X 0 0 0 X X 0 0 0 0 0 X X X 0 X X 0 X 0 X X 0 X 0 0 0 0 X 0 0 0 X X 0 0 0 X X 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X X X X 0 X 0 0 X X 0 X X X X 0 X X X 0 X 0 0 X X X X X 0 0 X 0 X 0 X X X X 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X 0 X X 0 0 0 X X 0 X X 0 X 0 0 0 X 0 0 X 0 X 0 X X 0 0 0 X X X X X X 0 X X X X 0 0 X X X X X 0 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 0 X 0 0 X X 0 X 0 X X 0 0 0 X 0 0 X X 0 X 0 0 0 X X X X 0 X 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 0 0 0 X X 0 X 0 X X X X X 0 X 0 X 0 X X 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 X 0 X X X X 0 X 0
generates a code of length 67 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+57x^56+48x^57+107x^58+136x^59+199x^60+214x^61+229x^62+256x^63+234x^64+272x^65+264x^66+268x^67+220x^68+232x^69+196x^70+236x^71+181x^72+188x^73+148x^74+92x^75+91x^76+66x^77+57x^78+36x^79+29x^80+4x^81+16x^82+10x^84+6x^86+2x^88+1x^90
The gray image is a linear code over GF(2) with n=134, k=12 and d=56.
This code was found by Heurico 1.16 in 2.74 seconds.