The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X 1 X X 1 1 X
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X 0 X X 0 X X 0 X X X X X X 0 0 0 X 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 X 0 0 X X 0 0 0 X X X X X X 0 X X 0 0 0 0 X
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X 0 0 X X X 0 0 0 0 X X 0 0 X X X 0 0 X X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X 0 0 0 X 0 X X X X X X X 0 0 X 0 0 0 0 X 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 0 X X 0 0 X 0 0 X X X 0 0 X 0 X X 0 0 X X X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 X 0 X 0 0 X 0 X 0 0 X 0 X X 0 0 0 X X 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X 0 X 0 0 X X X 0 0 X X 0 X 0 X X 0 X X X X X
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X X X X X 0 0 X X 0 X 0 0 X 0 X X X 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 X X X 0 0 0 0 X X 0 X X 0 0 0 X X 0 X 0 X X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 X X X X 0 X X X X X 0
generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+109x^40+285x^44+36x^46+512x^48+336x^50+869x^52+504x^54+703x^56+144x^58+359x^60+4x^62+175x^64+55x^68+3x^72+1x^88
The gray image is a linear code over GF(2) with n=106, k=12 and d=40.
This code was found by Heurico 1.16 in 2.95 seconds.