The generator matrix

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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+178x^50+679x^52+1068x^54+1437x^56+1736x^58+2013x^60+2102x^62+2057x^64+1838x^66+1490x^68+924x^70+585x^72+216x^74+57x^76+2x^78+1x^116

The gray image is a linear code over GF(2) with n=124, k=14 and d=50.
This code was found by Heurico 1.10 in 10.9 seconds.