The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 0 1 1 1 X X 1 1 1 0 1 1 1 X 0 0 1 1 X X 1 1 1 0 1 X 1 1 X 0 X 1 0 1 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 0 1 X X 1 X 0 X 0 X 0 X X+1 X 1 1 1 1 X 1 0 X X+1 0 0 1 0 1 X 1 1 1 1 X X+1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 0 X X+1 X 1 1 1 1 X 0 1 1 0 X+1 X+1 0 X 1 X+1 0 1 0 1 1 0 1 1 X 0 X+1 X+1 X X+1 1 X 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X 0 X+1 X+1 1 X 1 1 1 X+1 1 0 X+1 0 X X+1 X 0 X+1 X X 0 X X+1 1 X+1 1 X X X+1 1 0 X+1 0 X 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X X X+1 X+1 X 1 0 1 X X 0 1 0 X 0 1 X+1 1 1 1 X+1 X 1 1 0 0 X 1 X+1 X+1 0 X 1 X 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 X 0 X X 0 X X X 0 X X 0 X X X X X X 0 0 X X 0 X X X X X X X 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X X X X 0 0 0 X X 0 0 X 0 X 0 0 0 0 X 0 X 0 X X X X X X X 0 X X X 0 0
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X 0 0 X 0 X 0 X X X 0 0 0
generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+74x^42+92x^43+198x^44+268x^45+369x^46+398x^47+434x^48+466x^49+437x^50+518x^51+520x^52+596x^53+533x^54+570x^55+509x^56+478x^57+442x^58+382x^59+300x^60+198x^61+169x^62+80x^63+71x^64+40x^65+23x^66+8x^67+14x^68+2x^69+1x^70+1x^88
The gray image is a linear code over GF(2) with n=106, k=13 and d=42.
This code was found by Heurico 1.16 in 7.15 seconds.