The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+78x^17+217x^18+422x^19+637x^20+962x^21+1401x^22+1846x^23+2525x^24+3046x^25+3380x^26+3580x^27+3442x^28+3108x^29+2546x^30+2012x^31+1421x^32+890x^33+609x^34+318x^35+161x^36+106x^37+37x^38+14x^39+5x^40+2x^41+2x^42

The gray image is a code over GF(2) with n=54, k=15 and d=17.
This code was found by Heurico 1.16 in 32.2 seconds.