The generator matrix

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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+38x^53+86x^54+114x^55+124x^56+136x^57+131x^58+120x^59+154x^60+120x^61+102x^62+114x^63+113x^64+122x^65+118x^66+118x^67+91x^68+72x^69+50x^70+36x^71+23x^72+22x^73+21x^74+10x^75+2x^76+2x^77+2x^80+2x^82+1x^84+2x^86+1x^88

The gray image is a linear code over GF(2) with n=124, k=11 and d=53.
This code was found by Heurico 1.16 in 1.34 seconds.