The generator matrix

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

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+51x^18+22x^19+165x^20+162x^21+372x^22+478x^23+688x^24+970x^25+1148x^26+1532x^27+1647x^28+1812x^29+1666x^30+1596x^31+1195x^32+1012x^33+712x^34+430x^35+355x^36+138x^37+136x^38+38x^39+36x^40+2x^41+8x^42+9x^44+2x^46+1x^50

The gray image is a linear code over GF(2) with n=58, k=14 and d=18.
This code was found by Heurico 1.16 in 8.31 seconds.