The generator matrix

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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+61x^52+82x^53+158x^54+214x^55+237x^56+256x^57+256x^58+248x^59+252x^60+248x^61+233x^62+270x^63+196x^64+240x^65+204x^66+184x^67+193x^68+162x^69+124x^70+90x^71+67x^72+32x^73+44x^74+16x^75+14x^76+4x^77+5x^78+2x^79+3x^80

The gray image is a linear code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.16 in 2.25 seconds.