The generator matrix

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

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+197x^52+434x^54+499x^56+510x^58+516x^60+436x^62+470x^64+384x^66+306x^68+216x^70+76x^72+30x^74+13x^76+6x^78+2x^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 2.92 seconds.