The generator matrix

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

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+73x^50+88x^51+153x^52+198x^53+198x^54+264x^55+248x^56+238x^57+247x^58+264x^59+242x^60+276x^61+250x^62+240x^63+226x^64+196x^65+186x^66+120x^67+128x^68+102x^69+48x^70+40x^71+20x^72+14x^73+21x^74+8x^75+4x^76+1x^80+1x^82+1x^84

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 2.13 seconds.