The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  X  0  X  X  0  0  1  X  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  1  1 X+1  1  X  X  1  1  X  1  0  0  X  1  1  0  0
 0  0  1  0  0  0  0  0  1  0  1  1  X X+1 X+1  0  1  0 X+1  X  1  0  1  0  X  X  0  0  0
 0  0  0  1  0  0  0  0  1  1  X X+1  0  1  1 X+1  0  1 X+1 X+1 X+1 X+1  0  1  1  1 X+1  0  0
 0  0  0  0  1  0  0  0  1  1 X+1  X  1  0 X+1  X  0  1  0 X+1  1  1  X X+1  0  1  0  X  0
 0  0  0  0  0  1  0  1  0 X+1 X+1  0  X X+1 X+1  0  X  0  1  1 X+1  X  1  1  1  0  X X+1  0
 0  0  0  0  0  0  1  1 X+1  X  0  1  1  0 X+1  1 X+1 X+1  X X+1  1  X  X  X  1  X  X X+1  0
 0  0  0  0  0  0  0  X  X  0  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  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+49x^18+164x^19+292x^20+494x^21+722x^22+1024x^23+1474x^24+1942x^25+2380x^26+2846x^27+3222x^28+3378x^29+3272x^30+2930x^31+2499x^32+1938x^33+1509x^34+1074x^35+628x^36+424x^37+238x^38+150x^39+74x^40+16x^41+22x^42+4x^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 1.11 in 14.2 seconds.