The generator matrix

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

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+120x^52+290x^54+295x^56+282x^58+261x^60+201x^62+204x^64+155x^66+101x^68+79x^70+40x^72+15x^74+2x^76+2x^78

The gray image is a linear code over GF(2) with n=120, k=11 and d=52.
This code was found by Heurico 1.16 in 0.526 seconds.