The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  1  X  1  X  1  0  1  X  0  1  X  X  1  X  1  1  X  1  1  1  0  X  X  0  1  X  X  1  1  1  1  1  0  0  0  1  1  0  0  0  1  1  1  X  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  X  1 X+1  1  1  1 X+1  1 X+1  X  1  X  1  1 X+1  1  0 X+1  X  1  0  X  X  1  1  X  1  1  0  1  X  0  X  0  1  1  X  1 X+1  0  0  1  0  1  X  1  0  0
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  0  0  X X+1 X+1 X+1 X+1  0  1  X X+1  0  1 X+1 X+1 X+1  X  1  1 X+1  X  1  0  1  X X+1  0  X  X  1  1  X  0  0 X+1  1  X X+1  1  1  1  X  0 X+1 X+1  X  0
 0  0  0  1  0  0  X  1 X+1  1  0  1  1  0 X+1  1  X X+1  0 X+1  1  1  0  X  1  0 X+1  0 X+1  0  X  1  X  0  X  X  1  1  1 X+1  X  1  X X+1  X  X  X  0  1  0  1  X X+1 X+1  X X+1  X  X X+1  0
 0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  X  1  1  0  X  1  1  0  0  1 X+1  X  1  X  0  X X+1  1  1 X+1  X  0  1 X+1  1  1 X+1  1  X  X  0 X+1  X X+1 X+1  X  1  X  X  1  X  X  X X+1 X+1  X  0
 0  0  0  0  0  1  1  X  1  1 X+1  X  1  1 X+1  0  0  0  1  1  X X+1 X+1  X X+1  X X+1  1  X  0  1  X  X X+1 X+1  X  0  0 X+1  1 X+1  1  0 X+1 X+1  X  X X+1  1  1  0  0  0  1  1 X+1  0  X  X  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+66x^50+100x^51+156x^52+204x^53+221x^54+240x^55+265x^56+256x^57+230x^58+264x^59+236x^60+264x^61+248x^62+224x^63+187x^64+184x^65+169x^66+156x^67+134x^68+92x^69+83x^70+32x^71+43x^72+24x^73+6x^74+8x^75+2x^76+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 1.99 seconds.