The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  X  1  1  1  1  0  1  X  1  1  1  0  1  1  0  1  X  1  0  1  1  1  1  X  1  1  1  1  X  1  0  1  0  1  1  1  X  1  1  1  1  1  1  1  1  0  1  X
 0  1  1  0  1  1  0  1  1  X X+1  1  1  0 X+1  0 X+1  1 X+1  1  X  0 X+1  1 X+1  0  1  0  1 X+1  1 X+1  0  0  X  1  X X+1 X+1  0  1  X  1  X  1  1  1  1  1  0  0  1  1  X  0 X+1  X  1  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  X  0  X  0  X  0  X  X  0  0  X  X  X  0  0  X  X  X  X  0  X  X  0  X  X  X  X
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  0  X  X  X  X  X  X  X  X  0  X  X  0  0  0  X  0  X  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  0  0  X  X  X  X  X  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  X  X  X  X  X  0  X  X  X  0  X  0  X  X  0  X  X  X  X  X  0  X  X  X  X  X  0  0  0  X  0  X  X  X  0  X  0  0  0  0  0  X  0  X  X
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  0  X  0  X  0  0  0  X  X  X  X  0  X  0  X  X  0  X  0  0  X  X  X  0  X  0  X  X  0  0  X  0  X  0  0  X  0  0  0  X  0  X  0  X  X  X
 0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  0  X  0  X  0  X  X  X  X  0  0  0  0  X  X  X  0  X  X  0  X  0  0  X  0  0  X  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  0  X
 0  0  0  0  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  0  X  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  0  X  X  0  X  0  0  0  X  0  0  X  X

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+90x^52+68x^54+195x^56+108x^58+143x^60+92x^62+142x^64+116x^66+45x^68+9x^72+9x^76+5x^80+1x^84

The gray image is a linear code over GF(2) with n=120, k=10 and d=52.
This code was found by Heurico 1.16 in 0.188 seconds.