The generator matrix

 1  0  0  0  0  1  1  1  1  0  X  1  X  1  X  0  0  X  0  1  1  X  1  X  1  1  1  1  0  1  1  X  1  X  0  1  X  1  X  1  X  X  X  1  0  1  X  1  X  0  X  1  1  1  X  1  0  0  0  1  1  1
 0  1  0  0  0  0  0  0  X  0  0  X  X  0  1  1  1  1  1  1 X+1  1  1  1 X+1  1 X+1  X  0  X  1  1  1  1  1 X+1  0  0  X X+1  1  0  1  X  X  X  0  X  1  X  1 X+1 X+1  0  1  X  1  1  0  X  0  0
 0  0  1  0  0  0  0  1  1  1  X X+1  1  X  1  0  X  1  1  0  0 X+1 X+1  0  1  X  1 X+1  1  1  0  0  X  1  1  1  1 X+1  X X+1 X+1  1  X  X  X  1  1 X+1 X+1  1  0  X  1  X  1  1 X+1  0  1 X+1  0  1
 0  0  0  1  0  1  X  X  0  X  1 X+1  1 X+1  0  1  0 X+1  1  X X+1  X  1  1 X+1  X  0 X+1  1  X  0 X+1 X+1  X X+1  1  0  1  1  1  1 X+1  X  1  1  X  1  X X+1  X  X  1 X+1  0 X+1 X+1 X+1  0  X  1  0  X
 0  0  0  0  1  1  1 X+1  0  1 X+1  X  1  X  X  X X+1  0  1  0  0  1  1 X+1  X  1 X+1 X+1  X X+1  X  0  X  X X+1  X  1  0  0 X+1  0  X  0  0 X+1  1  X  1  1  0  1  X  X X+1  X  1  0  1  X  1  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  0  X  X  X  0  X  X  X  0  X  X  X  X  0  X  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+130x^54+282x^56+315x^58+291x^60+213x^62+212x^64+185x^66+153x^68+139x^70+67x^72+40x^74+16x^76+2x^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 0.553 seconds.