The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+96x^18+104x^19+357x^20+374x^21+559x^22+730x^23+981x^24+1188x^25+1340x^26+1678x^27+1423x^28+1660x^29+1447x^30+1326x^31+1040x^32+716x^33+569x^34+298x^35+270x^36+86x^37+78x^38+24x^39+22x^40+8x^41+7x^42+2x^44

The gray image is a code over GF(2) with n=56, k=14 and d=18.
This code was found by Heurico 1.16 in 9.3 seconds.