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 X 1 X 1 X X 1 1 1 1 1
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
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X X 0 X 0 0 X X X 0 X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X X 0 X 0 0 0 X 0 0 X X X X
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X 0 0 0 0 X 0 X X X 0 0 X 0 X X X 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 0 X X 0 0 0 X X 0 0 X 0 0 0 X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X 0 X 0 X 0 X X X 0 X 0 0 X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X X X 0 X 0 0 X X 0 X 0 X X 0 0 X X 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X X X X X 0 X 0 0 X X X 0 X X X 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 X 0 0 0 X 0 X 0 X X 0 0 0 0 0 X 0 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X 0 0 X X X 0 X X 0 0 X 0 0 X 0 0 0 0
generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+48x^24+95x^26+145x^28+169x^30+319x^32+741x^34+1007x^36+791x^38+359x^40+177x^42+119x^44+63x^46+39x^48+11x^50+9x^52+1x^54+1x^56+1x^64
The gray image is a linear code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 1.39 seconds.