The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  0  1  1  1  1  0  0  0  2  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  0  1  2  1  1  3  1  2  2  2  1  3  2  0  0  0
 0  0  1  0  0  0  1  1  1  1  1  0  0  3  3  2  0  3  0  3  1  2  1  3  3  0  3  0  0
 0  0  0  1  0  1  1  0  1  0  1  1  1  2  1  2  0  3  1  2  1  1  2  1  0  3  1  0  0
 0  0  0  0  1  1  0  1  1  0  1  1  0  2  0  3  3  2  3  2  0  1  3  3  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  0  2  2  0  0  2
 0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  2  0  0  0  2  2  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+44x^18+96x^19+277x^20+462x^21+712x^22+936x^23+1380x^24+1898x^25+2427x^26+2996x^27+3323x^28+3516x^29+3317x^30+3088x^31+2515x^32+1956x^33+1466x^34+968x^35+619x^36+342x^37+210x^38+104x^39+72x^40+18x^41+15x^42+4x^43+5x^44+1x^46

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 29.7 seconds.