The generator matrix

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

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+118x^18+216x^19+514x^20+840x^21+1358x^22+1956x^23+2885x^24+3752x^25+4942x^26+6068x^27+6436x^28+6964x^29+6684x^30+6236x^31+5093x^32+3812x^33+2799x^34+1956x^35+1314x^36+724x^37+462x^38+208x^39+141x^40+36x^41+20x^42+1x^50

The gray image is a linear code over GF(2) with n=58, k=16 and d=18.
This code was found by Heurico 1.11 in 58.5 seconds.