The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+52x^51+113x^52+150x^53+221x^54+228x^55+229x^56+238x^57+246x^58+248x^59+232x^60+254x^61+264x^62+228x^63+243x^64+252x^65+187x^66+200x^67+151x^68+106x^69+79x^70+56x^71+43x^72+22x^73+22x^74+12x^75+8x^76+2x^77+4x^78+4x^80+1x^82

The gray image is a linear code over GF(2) with n=122, k=12 and d=51.
This code was found by Heurico 1.16 in 2.23 seconds.