The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+70x^17+237x^18+436x^19+625x^20+926x^21+1345x^22+1914x^23+2564x^24+3032x^25+3415x^26+3532x^27+3394x^28+3176x^29+2578x^30+1912x^31+1451x^32+914x^33+563x^34+384x^35+149x^36+74x^37+53x^38+14x^39+8x^40+1x^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 29 seconds.