The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  X  X  0  1  1  1  1  0  1  1  0  1  1  0  X  1  X  1  1  1  1  X  1  1  1  1  0  1  1  1  0  1  0  X  X  1  0  1  0  X  1  0  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  1  0  X  1  1  X X+1  1  0  1  1  1  1  0  1  0  1  1  0  X X+1  X X+1  1  1  X  1 X+1  X  1 X+1  0  1  1  1  1  1 X+1  1  1  1  0 X+1  1  1 X+1  0
 0  0  1  0  0  0  1  1  1  X  1 X+1 X+1  1 X+1  1  X  0 X+1  X X+1  X X+1  0  X  X  0  1  0 X+1  0  1  1 X+1  1 X+1 X+1 X+1  1 X+1  X  X  X  0  1  0  0 X+1  1  X  1  1  X X+1  1 X+1 X+1 X+1  0  0
 0  0  0  1  0  1  1  0 X+1  X  0  X X+1 X+1  0  0 X+1  X  1  0  0 X+1  X  X  1 X+1  X  1  1  1  1 X+1 X+1  1  X X+1 X+1  X  X  X  X  1 X+1 X+1  0  1 X+1  1 X+1  0  1  0  1  0 X+1  X  1  0  1  0
 0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  X  0 X+1  0 X+1 X+1  X X+1  X  0 X+1 X+1  1 X+1  X X+1  1  0  X X+1  0  0  1  1 X+1  0  1  0 X+1  1  X  1  0  1  X  X X+1  1  0  0  0  X  X  1  1  X  0
 0  0  0  0  0  X  0  X  X  X  0  X  X  X  X  0  X  0  0  0  X  X  0  0  0  0  X  0  X  0  0  X  X  X  X  X  0  0  0  X  X  0  X  0  0  X  0  X  0  0  0  X  X  0  0  X  0  0  X  0
 0  0  0  0  0  0  X  0  X  0  X  X  0  0  X  X  0  X  0  X  0  X  0  0  X  0  X  0  0  0  0  X  X  X  0  X  X  X  0  X  0  X  X  X  0  X  X  X  0  0  X  X  X  X  X  0  0  X  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+52x^50+88x^51+126x^52+216x^53+254x^54+242x^55+257x^56+250x^57+256x^58+290x^59+263x^60+248x^61+213x^62+188x^63+221x^64+204x^65+157x^66+164x^67+123x^68+96x^69+73x^70+50x^71+28x^72+10x^73+19x^74+2x^75+4x^76+1x^80

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 2.01 seconds.