The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  1  1  1  1  1  X  1  1  1  X  X  0  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  X X+1 X+1  1  0 X+1 X+1  X  X X+1  0  1  0  1  0  0  0  X  0
 0  0  1  0  0  0  0  0  0  1 X+1 X+1  X X+1  1  X  1  1  1  1  X X+1  1 X+1  1  1 X+1  X  0
 0  0  0  1  0  0  0  1  1  1  1 X+1  1  X  X X+1  X  X X+1 X+1  X  0 X+1 X+1  X  0  X  0  0
 0  0  0  0  1  0  1  1  0  1  0  X  0  1  X X+1  1  1  1 X+1  0 X+1  X  0  X  X X+1 X+1  0
 0  0  0  0  0  1  1  0  1 X+1  0  1  0 X+1  1 X+1  0  X  0 X+1  1  1 X+1  1 X+1  0  X  1  0
 0  0  0  0  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0  X  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  X  X  X  0  0  X  X  0  X  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+64x^18+150x^19+304x^20+514x^21+662x^22+1046x^23+1495x^24+1904x^25+2348x^26+2862x^27+3214x^28+3340x^29+3424x^30+2964x^31+2458x^32+1960x^33+1404x^34+1034x^35+656x^36+450x^37+266x^38+134x^39+61x^40+24x^41+24x^42+2x^43+2x^44+1x^48

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 39.9 seconds.