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.