The generator matrix
1 0 0 0 1 1 1 1 0 1 X 1 X 1 X X X 1 1 1 1 0 X X 1 1 1 1 1 1 1 0 0 1 0 1 1 X 0 0 0 1 1 0 1 1 1 0 X X 0 0 1 1 1 1 X 1 X 1 1 1 1 0 X 1 1 0 1
0 1 0 0 0 1 1 X 1 X+1 1 1 1 X 0 1 1 X 1 X+1 X X 0 1 0 X+1 X+1 X X+1 1 0 1 0 X 1 0 X+1 X 1 1 1 0 X 1 0 0 1 1 X 0 0 1 X+1 0 X 0 X X+1 1 X X+1 1 X+1 1 1 X X 1 X
0 0 1 0 1 1 0 0 X+1 0 X X+1 1 1 1 X X+1 X X X+1 X X 1 1 X+1 0 X+1 X 1 0 X 0 1 X+1 0 X X 0 X 1 0 1 0 1 0 1 X 1 1 1 0 1 1 0 X+1 X+1 1 1 X+1 0 1 X+1 1 X X X+1 0 X+1 X+1
0 0 0 1 1 0 1 1 1 X 1 X+1 0 X 1 X+1 1 1 X+1 0 X 1 0 X X 1 X+1 1 1 0 0 X 0 X+1 1 X 0 1 0 X 0 1 1 1 X+1 X+1 X X+1 1 X 1 1 0 0 X 1 1 0 X+1 X+1 X+1 1 1 0 0 X X+1 X+1 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 0 X X X X 0 X X 0 X X 0 X X X X 0 0 X 0 X 0 X X 0 X X 0 0 X 0 X X 0 X X X 0 0 0 X X X X X 0 X
0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X 0 0 X X X 0 X X X 0 0 0 X X 0 0 X X X 0 X 0 X 0 0 0 X 0 0 0 0 0 0 X X X 0 0 0 X X 0 0 X X 0 X X X X
0 0 0 0 0 0 X 0 0 0 0 0 X X 0 0 0 0 X 0 0 0 X X X 0 0 X X X X X 0 X X X X 0 X X 0 X 0 0 X 0 X X 0 X X 0 X X 0 0 X X X 0 X 0 0 X 0 X X X X
generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 60.
Homogenous weight enumerator: w(x)=1x^0+48x^60+64x^61+119x^62+146x^63+128x^64+158x^65+119x^66+136x^67+134x^68+124x^69+122x^70+100x^71+115x^72+102x^73+82x^74+78x^75+51x^76+42x^77+42x^78+32x^79+22x^80+20x^81+18x^82+18x^83+11x^84+2x^85+9x^86+2x^87+2x^88+1x^90
The gray image is a linear code over GF(2) with n=138, k=11 and d=60.
This code was found by Heurico 1.16 in 0.641 seconds.