The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+78x^50+138x^51+236x^52+316x^53+367x^54+394x^55+397x^56+486x^57+438x^58+462x^59+585x^60+492x^61+464x^62+540x^63+493x^64+470x^65+402x^66+372x^67+302x^68+238x^69+189x^70+128x^71+93x^72+44x^73+41x^74+12x^75+5x^76+2x^77+4x^78+2x^79+1x^90

The gray image is a linear code over GF(2) with n=122, k=13 and d=50.
This code was found by Heurico 1.16 in 8.77 seconds.