The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  0  X  1  1  0  X  1  1  1  1  1  1  0  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1 X+1  1  1  X  X  1  1 X+1  1 X+1  0  X X+1  X  0  0
 0  0  1  0  0  0  1  1  1  1  1  0  0 X+1  1 X+1  1  X  X  1 X+1  0  0  0  0  0  0  X  0
 0  0  0  1  0  1  1  0  1  0  1  1  1  1  1  0  X  1  X  1  0 X+1  0  1  X  0  1  0  0
 0  0  0  0  1  1  0  1  1  0  1  1  0  X  0  1  0 X+1  1  1  1 X+1  0  X X+1  1  0  1  0
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  0  0  X  0  X  X  0  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  0  0  X  0  0  X  X  X  0  0  X  0  0

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+76x^18+128x^19+314x^20+472x^21+728x^22+1020x^23+1464x^24+1910x^25+2390x^26+2982x^27+3106x^28+3416x^29+3264x^30+2880x^31+2547x^32+1956x^33+1464x^34+1060x^35+686x^36+416x^37+248x^38+116x^39+68x^40+22x^41+22x^42+6x^43+6x^44

The gray image is a linear code over GF(2) with n=58, k=15 and d=18.
This code was found by Heurico 1.16 in 29.6 seconds.