The generator matrix

 1  0  0  0  0  1  1  1  1  0  X  1  X  1  1  0  1  1  X  1  0  1  1  1  X  0  X  X  0  1  X  1  1  1  1  X  0  0  0  1  1  1  1  0  X  0  0  X  0  X  1  1  1  0  1  1  1  1  X  X
 0  1  0  0  0  0  0  0  X  0  0  X  X  1 X+1  1 X+1  1  0 X+1  1  1 X+1  1  1  1  1  1  0  X  1  1  X  1  1  1  X  0  X  X  0 X+1  X  0  1  X  1  X  1  1 X+1  X  0  1  X  X  1 X+1  1  X
 0  0  1  0  0  0  0  1  1  1  X X+1  1  1  X  X X+1  X  1  X X+1  1  0 X+1  X X+1  1  0  1  0  1  0  0  1  0 X+1  X  0  0 X+1  1  1 X+1  X X+1  1  0  X  1  0 X+1  1  0  X X+1  1 X+1  X X+1  1
 0  0  0  1  0  1  X  X  0  X  1 X+1  1  0  0 X+1  1 X+1  1  X X+1 X+1 X+1  0 X+1  1  X  X  1 X+1  1  X  0  1  1  X  1  X  1  0 X+1  1  1  X X+1  0 X+1  1  X X+1  X  1 X+1  X  0  X X+1  1  X  X
 0  0  0  0  1  1  1 X+1  0  1 X+1  X  1  X X+1  0  1  X  0  0  1  0  1  1 X+1  X  0 X+1  1  0  1  X X+1  X  0  1  1  1  X  1  1  X  X  1 X+1  1  0 X+1 X+1  1  0  X X+1  1  0 X+1  1  0 X+1 X+1
 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  X  X  X  X  X  X  0  X  X  X  0  0  0  0  0  X  X  0  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+117x^52+268x^54+347x^56+276x^58+231x^60+180x^62+247x^64+144x^66+111x^68+72x^70+27x^72+20x^74+5x^76+2x^80

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 0.534 seconds.