The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^16+68x^17+217x^18+320x^19+668x^20+880x^21+1281x^22+1932x^23+2478x^24+3160x^25+3575x^26+3664x^27+3240x^28+3120x^29+2519x^30+1992x^31+1471x^32+900x^33+559x^34+272x^35+220x^36+64x^37+39x^38+12x^39+34x^40+1x^42+1x^46

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 21.6 seconds.