The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+183x^20+456x^22+645x^24+710x^26+851x^28+674x^30+393x^32+138x^34+37x^36+6x^38+1x^40+1x^44

The gray image is a code over GF(2) with n=54, k=12 and d=20.
This code was found by Heurico 1.16 in 0.628 seconds.