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 1 X X X X X X X X X 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 X 0 X 0 0 0 0 X 0 X X X 0 X 0 X X 0 X 0 X
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 X 0 X 0 0 0 X X 0 X X 0 X 0 X 0 X X X 0 X 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 X X 0 X X 0 0 0 X X X 0 X 0 0 X X X X 0 0 0 X 0 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 0 0 0 0 X X X X 0 0 0 X 0 X X 0 X 0 X 0 X 0 0 X X
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 0 X X 0 0 0 0 0 0 X 0 X 0 X 0 X X X 0 X 0 0 0 0 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 0 0 X X 0 0 X X X 0 0 0 0 X 0 0 X 0 X 0 X X 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 X X X 0 X 0 X X X X X 0 0 0 0 0 0 X 0 0 0 0 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 X 0 X X X 0 X X X 0 X 0 X X 0 X 0 X X X X X 0 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 0 0 X X 0 X X X X X X 0 X X 0 X 0 0 0 0 X X 0
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 X 0 0 0 X 0 0 0 0 0 0 X 0 X X X 0 X X X 0 X 0 X X
generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+166x^40+4x^42+343x^44+84x^46+598x^48+424x^50+838x^52+424x^54+668x^56+84x^58+289x^60+4x^62+133x^64+33x^68+2x^72+1x^84
The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 2.97 seconds.