The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+72x^16+148x^18+40x^19+120x^20+162x^22+480x^23+264x^24+276x^26+1008x^27+200x^28+220x^30+480x^31+291x^32+180x^34+40x^35+48x^36+18x^38+28x^40+20x^42

The gray image is a code over GF(2) with n=54, k=12 and d=16.
This code was found by Heurico 1.16 in 0.505 seconds.