The generator matrix

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

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+137x^54+270x^56+310x^58+276x^60+232x^62+247x^64+174x^66+154x^68+115x^70+64x^72+44x^74+10x^76+12x^78+2x^80

The gray image is a linear code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.16 in 0.588 seconds.