The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  1  1  0  X  0  1  0  1  X  X  1  1
 0  1  0  0  0  1  1  1  0  0  1 X+1  1  1  X  1  1  X  0  0  1  1  X  0  1  1  1 X+1  X
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  X X+1  1  1  0  1  X  X  1  0  X X+1  X  1
 0  0  0  1  1  0  1  1  1  0  1  0  1  X X+1 X+1 X+1  X  1  1  0  1  0  X  0  X X+1  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  0  X  0  X  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  X  0  X  X  0  0  0  X  0  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  X  X  X  X  X  X  0  X  X  0  X  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  X  X  0  0  0  0  X  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  0  X  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  0  X  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+84x^19+328x^20+370x^21+691x^22+826x^23+1445x^24+1974x^25+2408x^26+3234x^27+3168x^28+3492x^29+3331x^30+3060x^31+2426x^32+2012x^33+1428x^34+936x^35+752x^36+330x^37+233x^38+50x^39+63x^40+14x^41+24x^42+2x^43+8x^44+1x^46+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 28.5 seconds.