The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+52x^18+110x^19+203x^20+250x^21+395x^22+500x^23+564x^24+728x^25+825x^26+844x^27+823x^28+828x^29+618x^30+536x^31+391x^32+216x^33+146x^34+54x^35+61x^36+26x^37+11x^38+4x^39+4x^40+1x^42+1x^44

The gray image is a code over GF(2) with n=54, k=13 and d=18.
This code was found by Heurico 1.16 in 2.17 seconds.