The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1  0  X  0  1  0  1  X  X  X  1  X  X  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0 X+1  1  1  X  1  X  1  1  X  X  1  X  1  1  0  0
 0  0  1  0  0  0  0  0  1  0 X+1  1  X  X X+1  1  1  0 X+1  0  1  X  0  0 X+1 X+1 X+1 X+1  0
 0  0  0  1  0  0  0  0  1 X+1  1  X X+1  1  0 X+1  0  X  X X+1  1  X  0  X  X  1  X  X  0
 0  0  0  0  1  0  0  0  1 X+1  X  1  1  0  X  1  1  X  X  1  X  1  0  1  1  0  1  1  0
 0  0  0  0  0  1  0  1  1  X  X X+1  X  1  X  1 X+1  0 X+1  X X+1  1  1  0 X+1  X  X X+1  0
 0  0  0  0  0  0  1  1  X  1 X+1  0  X  0 X+1  0 X+1 X+1  1  X X+1  X X+1  X X+1 X+1  0 X+1  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  0  X  X  X  0  0  X  X  0  0  0  0  X  X  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+64x^18+144x^19+304x^20+420x^21+794x^22+1034x^23+1445x^24+2006x^25+2300x^26+2928x^27+3214x^28+3326x^29+3272x^30+2934x^31+2433x^32+2018x^33+1508x^34+1010x^35+712x^36+406x^37+238x^38+136x^39+81x^40+16x^41+16x^42+6x^43+2x^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 39.8 seconds.