The generator matrix

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

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+41x^52+114x^53+164x^54+198x^55+226x^56+238x^57+248x^58+272x^59+270x^60+252x^61+253x^62+250x^63+220x^64+218x^65+197x^66+202x^67+178x^68+132x^69+127x^70+80x^71+77x^72+56x^73+31x^74+22x^75+11x^76+14x^77+4x^78

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 2.1 seconds.