The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+79x^16+116x^17+219x^18+414x^19+712x^20+954x^21+1461x^22+1976x^23+2361x^24+2976x^25+3298x^26+3380x^27+3320x^28+3100x^29+2538x^30+2056x^31+1476x^32+956x^33+623x^34+350x^35+224x^36+90x^37+49x^38+16x^39+19x^40+4x^42

The gray image is a code over GF(2) with n=54, k=15 and d=16.
This code was found by Heurico 1.16 in 24 seconds.