The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  1  1  0  0  1  1  1  1  2  0  1  2  2  1  2  0  1
 0  1  0  0  0  0  0  0  0  1  2  3  3  1  1  2  0  3  3  0  0  2  2  1  1  3  1  1  0
 0  0  1  0  0  0  0  0  0  1  3  3  2  3  0  1  1  2  1  1  1  1  2  1  2  0  0  0  0
 0  0  0  1  0  0  0  1  1  1  0  2  2  3  3  0  2  0  0  2  3  1  1  2  3  0  0  0  0
 0  0  0  0  1  0  1  1  0  1  1  3  1  0  2  1  1  1  2  2  2  1  3  3  3  0  2  2  0
 0  0  0  0  0  1  1  0  1  1  0  3  0  3  3  3  1  1  1  0  1  3  1  2  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  0  2  2  2  2  0  2  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  0  2  0  2  2  0  2  2  0  0  2  2  0  0

generates a code of length 29 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+56x^18+132x^19+338x^20+436x^21+767x^22+1114x^23+1358x^24+1890x^25+2397x^26+2936x^27+3256x^28+3336x^29+3222x^30+2900x^31+2479x^32+2068x^33+1474x^34+1012x^35+674x^36+436x^37+251x^38+98x^39+82x^40+26x^41+25x^42+4x^44

The gray image is a code over GF(2) with n=58, k=15 and d=18.
This code was found by Heurico 1.16 in 32.5 seconds.