The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 X 1 1 1 1 1 1 X 1 X 1 1 X 1 1 1 0 1 1 1 X 1 X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X X 0 X X X X 0 0 0 0 0 0 X 0 X 0 X X X 0 X 0 X X X X X 0 0 X X 0 0 X X 0 X 0 0 0 X 0 X 0 X 0 0 X X X X X 0 0
0 0 X 0 0 0 0 0 0 0 X X X 0 0 0 0 X X X X 0 0 X 0 0 0 X X 0 X X 0 X 0 0 0 0 0 X X X X X X X 0 X 0 0 X X X X X X X 0 X 0 X 0 X X X X X X X
0 0 0 X 0 0 0 0 0 X X X X X X X 0 0 0 0 X X X 0 0 X X 0 0 X 0 0 0 0 X 0 X X 0 X 0 0 X 0 0 X X 0 X X X X 0 0 0 X X X 0 X X X X 0 0 X X X X
0 0 0 0 X 0 0 0 0 X 0 0 X 0 0 X 0 0 0 X 0 X X X 0 X 0 X 0 X X 0 X X 0 X 0 X 0 X 0 X X 0 0 X 0 X 0 X X X X 0 0 0 0 0 X 0 X X X X 0 0 0 0 0
0 0 0 0 0 X 0 0 0 X 0 X X 0 X X X X X 0 0 0 0 0 0 X 0 0 X 0 0 0 X X X X 0 0 X X 0 0 X X X 0 0 X 0 0 0 X X 0 0 X 0 X X 0 X 0 0 X 0 X 0 0 X
0 0 0 0 0 0 X 0 0 X 0 X 0 X 0 0 0 X 0 0 0 X X X X 0 X X 0 0 X 0 0 X X 0 X 0 X X 0 0 X X 0 0 0 0 X X X 0 X 0 X 0 0 X 0 0 X 0 0 X 0 0 X X X
0 0 0 0 0 0 0 X 0 X X 0 0 0 X 0 0 0 X 0 0 X X X X X 0 0 X X 0 0 X X X 0 0 X X 0 0 X X 0 0 0 X 0 0 0 X 0 X X X X X X X 0 0 0 X X X X 0 X X
0 0 0 0 0 0 0 0 X X X 0 X X X 0 X X 0 X 0 0 X 0 0 0 0 X X 0 X X X X 0 0 X X X 0 0 0 X 0 0 0 X X 0 0 X X 0 X X 0 0 X X X 0 X X 0 0 X X X 0
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+99x^60+12x^62+157x^64+76x^66+219x^68+132x^70+143x^72+36x^74+74x^76+44x^80+23x^84+6x^88+1x^92+1x^120
The gray image is a linear code over GF(2) with n=138, k=10 and d=60.
This code was found by Heurico 1.16 in 0.472 seconds.