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

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+65x^52+100x^53+160x^54+196x^55+240x^56+238x^57+235x^58+252x^59+240x^60+284x^61+217x^62+260x^63+247x^64+220x^65+215x^66+214x^67+179x^68+126x^69+118x^70+86x^71+76x^72+52x^73+38x^74+14x^75+8x^76+2x^77+8x^78+2x^79+2x^81+1x^86

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 2.04 seconds.