The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+231x^52+370x^54+490x^56+548x^58+531x^60+446x^62+484x^64+336x^66+305x^68+190x^70+120x^72+28x^74+13x^76+2x^78+1x^80

The gray image is a linear code over GF(2) with n=122, k=12 and d=52.
This code was found by Heurico 1.16 in 38.4 seconds.