The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+113x^18+180x^19+406x^20+512x^21+722x^22+960x^23+1152x^24+1500x^25+1662x^26+1792x^27+1696x^28+1640x^29+1256x^30+1016x^31+735x^32+416x^33+313x^34+140x^35+106x^36+24x^37+30x^38+8x^39+4x^41

The gray image is a code over GF(2) with n=54, k=14 and d=18.
This code was found by Heurico 1.16 in 64.8 seconds.