The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 1 1 0 X 1 1 0 X X 0 1 1 1 1 0 X 1 1 0 1 X X 0 X X X X X 1 0 X 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 1 0 X 1 0 X+1 1 0 X 1 X 0 1 1 X+1 X X 1 X+1 0 0 X 1 0 1 X 1 1 0 X+1 0 1 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 1 X 1 0 0 0 0 X+1 1 1 X X X+1 0 X X 0 1 0 0 X 0 1 0 1 1 0 X X+1 X X 1 0 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 1 X 1 X+1 X 1 X X+1 X 0 X+1 0 X X+1 0 X+1 1 0 X 1 1 X+1 X+1 0 1 X+1 X X 1 1 X 0 0 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X 1 0 X+1 1 X+1 X X X+1 1 1 X 0 X+1 1 0 0 0 1 0 1 0 1 X+1 1 1 1 X+1 X+1 1 0 X 0 0
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 0 1 X+1 X+1 X 0 0 0 X+1 0 X+1 1 0 X 1 X X+1 X+1 1 0 1 X 1 1 X+1 X 1 1 0 X X+1 1 X+1 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+61x^52+90x^53+166x^54+204x^55+217x^56+286x^57+233x^58+250x^59+253x^60+252x^61+238x^62+230x^63+232x^64+218x^65+198x^66+220x^67+224x^68+132x^69+124x^70+84x^71+54x^72+40x^73+29x^74+34x^75+14x^76+6x^77+4x^78+2x^79

The gray image is a linear code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.10 in 0.765 seconds.