The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 X 1 X 1 1 1 0 1 1 1 X X X 1 1 1 X 1 0 0 1 0 1 1 1 1 1 0 X 0 1 X 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 1 X+1 1 1 0 1 X X 0 0 1 1 1 1 1 1 0 1 0 X X 1 X X X 1 0 1 1 1 X 1 0 X+1 0
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 X X 1 1 0 1 1 0 X 1 0 1 X+1 0 1 1 1 X+1 1 1 0 X 1 0 X 0 1 1 0 X+1 X+1 X 1 X 0
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 0 0 0 X X 0 X X 0 X X X X X 0 X X X X 0 0 X 0 0 X X X
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 0 X 0 0 X X 0 X X X X 0 0 X 0 0 0 X X X 0 0 0 0 X 0 0 X X 0 0 0 X X
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X X X X 0 X X 0 0 X X 0 X 0 X X 0 0 0 0 0 0 0 X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X 0 X X X 0 X 0 X 0 X X X 0 X X 0 X X X 0 X X X 0 0 0 0 X X 0 0 X
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X 0 X 0 X 0 0 X X X 0 X 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X X X X 0 0 0 0 X 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 X X 0 0 X 0 X 0 0 0 0 X X X 0 X 0 X 0 X 0 X 0 0 X 0 0 0 X X 0 X
generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+205x^44+310x^46+514x^48+484x^50+597x^52+472x^54+588x^56+404x^58+299x^60+114x^62+77x^64+8x^66+19x^68+4x^72
The gray image is a linear code over GF(2) with n=106, k=12 and d=44.
This code was found by Heurico 1.16 in 92.5 seconds.