The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 1 1 0 1 0 1 X X X 1 1 1 X 1 X 1 0 1 0 X 1 1 1 1 0 0 0 1
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X+1 X X 1 1 1 0 X+1 X+1 1 X+1 0 X X+1 1 X 0 1 1 0 X X+1 X X X X X X+1 0 1 X 1 0 0 1 1 X 0
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 X 1 0 1 X+1 1 0 X X+1 1 1 0 1 1 X 0 X 1 0 X X 1 0 X+1 1 1 X X X 1 0
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X 0 X+1 1 X 0 X 1 1 X+1 X+1 1 X+1 X X X+1 0 X+1 1 0 0 0 X 1 1 X X 1 X 0 X 1 1 1 X+1 X+1 X+1 1 0
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 1 X X X+1 1 0 X+1 0 X+1 1 X 0 X+1 X+1 X 0 X 1 0 0 1 1 X+1 X+1 0 0 X+1 0 X+1 1 1 X+1 0 0 X+1 X X+1 0
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X X+1 0 X+1 0 X+1 0 1 0 X X+1 1 X X+1 0 1 1 1 X+1 X X+1 0 0 X+1 X 0 X+1 0 X 0 X 0 X+1 1 0 0 X+1 1 0
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X 0 0 0 X 0 X X X X 0 0 0 0 X X X 0 0 X X X 0 X 0 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+80x^42+88x^43+205x^44+296x^45+311x^46+368x^47+418x^48+504x^49+533x^50+514x^51+513x^52+550x^53+504x^54+592x^55+519x^56+428x^57+431x^58+396x^59+306x^60+240x^61+170x^62+80x^63+74x^64+28x^65+16x^66+10x^67+12x^68+2x^69+2x^70+1x^86

The gray image is a linear code over GF(2) with n=106, k=13 and d=42.
This code was found by Heurico 1.10 in 2.33 seconds.