The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 X X 1 X 1 X 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X X X 0 X X 0 0 0 X X X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 X X X 0 0 X 0 0 X
0 0 0 0 X 0 0 0 0 0 0 0 0 X X 0 X X X X X X 0 X X X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 X 0 X 0 X 0 X 0 X 0 X 0 X 0 X
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X 0 X 0 0 X 0 X X 0 X 0 0 X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 X 0 X X X X X 0 X 0 0 0 0 X
0 0 0 0 0 0 0 0 X 0 0 X 0 0 X 0 X X 0 0 X X X 0 0 X 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X X X X 0 X X X X 0 0 X 0 X
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X 0 0 0 X 0 0 X X X 0 X X
generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+47x^18+120x^20+146x^22+32x^23+169x^24+192x^25+223x^26+480x^27+284x^28+640x^29+326x^30+480x^31+274x^32+192x^33+189x^34+32x^35+136x^36+70x^38+35x^40+21x^42+4x^44+2x^46+1x^48
The gray image is a linear code over GF(2) with n=58, k=12 and d=18.
This code was found by Heurico 1.16 in 2.76 seconds.