The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+189x^18+713x^20+1399x^22+2407x^24+3420x^26+3466x^28+2590x^30+1425x^32+549x^34+173x^36+43x^38+7x^40+2x^42

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 20.4 seconds.