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

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+286x^42+738x^44+1158x^46+1690x^48+2042x^50+2213x^52+2282x^54+2234x^56+1612x^58+1190x^60+596x^62+250x^64+84x^66+3x^68+4x^70+1x^96

The gray image is a linear code over GF(2) with n=106, k=14 and d=42.
This code was found by Heurico 1.10 in 8.95 seconds.