The generator matrix
1 0 0 0 0 0 0 0 1 1 1 1 X 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 X 1 1 0 1 X X 1 0 X 1 X 1 0 1 1 1 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 X+1 1 0 0 0 1 1 1 1 X+1 1 X X 1 X+1 1 1 X+1 X X 1 1 1 1 X X X 1 1 1 0 1 1 X 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 X+1 1 X 1 X 1 X+1 X X+1 X+1 X+1 X+1 0 X+1 X+1 0 X X X+1 1 X+1 X 0 0 X X X 0 0 X 1 X+1 0 1
0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 X+1 X+1 1 1 X+1 X 1 X+1 X X X X+1 X+1 X X 1 0 X+1 1 1 0 1 0 1 X+1 1 1 0 X 1 0 0 X 1 1 1
0 0 0 0 1 0 0 0 1 0 X X+1 1 X 0 1 1 1 X+1 0 X+1 X X X+1 1 1 0 0 0 0 X X+1 X X 0 0 X 0 X+1 1 X+1 1 X X X X+1 1 X X+1 X+1 1
0 0 0 0 0 1 0 0 1 X X+1 X 1 0 0 X 0 0 1 X X X 1 1 1 X+1 1 X 1 1 X 1 X+1 X X+1 0 0 X+1 X+1 1 X 1 1 1 X+1 0 1 X 0 X+1 0
0 0 0 0 0 0 1 0 1 X+1 0 X X+1 X X X X 0 1 1 X+1 1 X 1 1 0 X 1 0 X+1 X+1 X X+1 0 X+1 0 X+1 1 X+1 X+1 0 0 1 X 1 1 0 1 X X+1 0
0 0 0 0 0 0 0 1 X 1 X+1 X+1 X+1 1 1 X+1 1 X 0 0 0 1 X X X+1 0 X X+1 0 X+1 X 1 X+1 0 X+1 X X X 0 1 1 X+1 X X X 0 X 0 1 1 1
generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.
Homogenous weight enumerator: w(x)=1x^0+346x^38+1263x^40+2396x^42+3976x^44+6052x^46+8389x^48+10066x^50+10085x^52+9036x^54+6507x^56+3840x^58+2122x^60+900x^62+379x^64+130x^66+41x^68+2x^70+4x^72+1x^80
The gray image is a linear code over GF(2) with n=102, k=16 and d=38.
This code was found by Heurico 1.11 in 160 seconds.