The generator matrix

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

generates a code of length 63 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+50x^53+120x^54+174x^55+203x^56+232x^57+243x^58+224x^59+259x^60+242x^61+231x^62+250x^63+249x^64+250x^65+224x^66+220x^67+185x^68+172x^69+143x^70+122x^71+110x^72+62x^73+56x^74+28x^75+16x^76+16x^77+6x^78+6x^79+1x^80+1x^82

The gray image is a linear code over GF(2) with n=126, k=12 and d=53.
This code was found by Heurico 1.16 in 2.2 seconds.