The generator matrix

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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+51x^54+161x^56+114x^58+160x^60+83x^62+174x^64+84x^66+125x^68+37x^70+12x^72+6x^74+2x^76+5x^78+3x^80+4x^82+1x^84+1x^88

The gray image is a linear code over GF(2) with n=124, k=10 and d=54.
This code was found by Heurico 1.16 in 0.199 seconds.