The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^18+90x^19+313x^20+334x^21+688x^22+882x^23+1442x^24+1974x^25+2437x^26+3156x^27+3200x^28+3580x^29+3247x^30+3028x^31+2436x^32+1980x^33+1478x^34+978x^35+721x^36+310x^37+238x^38+58x^39+72x^40+14x^41+17x^42+6x^44+3x^46+1x^48

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 86.1 seconds.