The generator matrix

 1  0  0  1  1  1  0  1  1  1  0  1  0  X  1  1  1  0  X  1  0  0  1  1  X  1  1  X  1  1  1  0  0  0  X  1  1  1  1  1  1  1  0  X  1  X  X  1  X  1  1  0  0  0  1  X  1  1  X  1
 0  1  0  0  1  1  1  0  X  1  0 X+1  1  1  X  1 X+1  1  0  X  1  1  0  0  0  1  1  1  X  X X+1  1  X  0  1 X+1  1  X  X  0  1 X+1  0  1  1  X  1 X+1  X  0  X  1  1  0 X+1  1  0  X  1  0
 0  0  1  1  1  0  1  0  1 X+1  1  0  X  1  1 X+1  X  0  1  X  1  0  X X+1  1  X X+1 X+1  X  0  0  0  1  1  0  0 X+1 X+1  1  X X+1  X  1  0  X  1  1  0  1  0  X  X X+1  1 X+1  1 X+1  X  X  1
 0  0  0  X  0  0  0  0  0  X  X  0  0  X  X  0  0  X  X  X  0  X  X  X  X  0  0  0  0  X  0  X  X  0  X  0  0  0  X  X  0  X  0  0  X  X  0  0  X  0  0  0  X  0  0  X  X  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  X  0  X  X  X  X  0  0  0  X  X  0  0  X  0  0  X  X  0  0  X  0  0  X  X  0  0  0  X  X  X  0  X  0  0  X  X  X  X  X  X  0  0  0  X
 0  0  0  0  0  X  0  0  X  0  X  0  X  0  0  0  X  0  0  0  X  X  X  0  0  0  X  0  X  X  0  X  X  X  0  X  0  0  0  0  X  X  X  0  0  X  0  X  X  X  X  0  0  X  0  X  X  0  X  X
 0  0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  0  X  X  X  X  0  0  X  0  X  0  X  X  0  X  0  0  0  X  0  0  0  X  0  X  X  X  X  X  0  0  X  X  0  0  0  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  X  X  X  X  X  0  0  X  X  0  0  0  X  0  0  X  X  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  X  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+158x^52+202x^54+352x^56+270x^58+268x^60+200x^62+200x^64+160x^66+111x^68+62x^70+54x^72+2x^74+6x^76+1x^80+1x^84

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 0.607 seconds.