The generator matrix

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

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+111x^50+291x^52+410x^54+512x^56+506x^58+530x^60+540x^62+410x^64+356x^66+235x^68+102x^70+50x^72+18x^74+16x^76+4x^78+3x^80+1x^82

The gray image is a linear code over GF(2) with n=120, k=12 and d=50.
This code was found by Heurico 1.16 in 3.82 seconds.