The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 1 X 0 1 1 1 X 1 0 X 1 X 1 1 1 1 0 X X X 1 1 X 0 1 X X 1 1 1 1 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 X+1 1 1 1 X 1 0 0 1 1 X 1 1 X+1 X+1 0 X 1 1 0 X X 1 X X+1 1 1 X+1 0 X+1 X+1 X X+1 X
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 0 1 0 1 1 X+1 1 X+1 X 1 0 1 X+1 X+1 1 0 1 X+1 X 1 0 1 0 1 X 0 X 1 X+1 X 1 1 1 1
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 X 0 0 0 X X X X X X 0 0 0 X X X X 0 X X X 0 X X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 X X X X 0 0 X 0 0 0 X X 0 0 0 0 X 0 0 X X 0 X X X X 0 X 0 0 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X X X X X 0 0 X X X X X 0 0 X X 0 0 X 0 X 0 0 X 0 X X X X 0 X
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X 0 X X 0 0 0 X X X X X X 0 X 0 X 0 X X X X 0 0 0 X 0 X 0 0 X 0 0 X
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0 0 X 0 0 X X 0 X 0 X 0 X X X 0 0 X 0 X 0 0 X 0 X X X X 0 X X X X
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 X X X 0 0 0 0 X X 0 X 0 X X X 0 0 X X 0 0 0 0 0 0 0 X X X 0 0 X X
generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+70x^42+68x^43+124x^44+150x^45+208x^46+230x^47+269x^48+280x^49+223x^50+288x^51+272x^52+340x^53+281x^54+276x^55+229x^56+184x^57+160x^58+140x^59+96x^60+70x^61+70x^62+22x^63+26x^64+11x^66+4x^68+1x^70+3x^72
The gray image is a linear code over GF(2) with n=104, k=12 and d=42.
This code was found by Heurico 1.16 in 2.32 seconds.