The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+51x^16+20x^17+143x^18+172x^19+362x^20+466x^21+751x^22+974x^23+1216x^24+1528x^25+1578x^26+1800x^27+1553x^28+1636x^29+1230x^30+988x^31+766x^32+420x^33+355x^34+156x^35+132x^36+26x^37+35x^38+6x^39+14x^40+4x^42+1x^44

The gray image is a code over GF(2) with n=54, k=14 and d=16.
This code was found by Heurico 1.16 in 12.2 seconds.