The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  1  1  1  1  2  0  2  1  1  0  0  1  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  2  0  0  1  3  1  1  1  3  1  1  0  0  0
 0  0  1  1  1  0  1  0  1  1  0  2  1  1  0  3  3  0  1  0  1  0  1  2  1  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  2  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  2  2  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  2  0  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  2  2  0  0  2  0  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+200x^16+234x^18+732x^20+1294x^22+2660x^24+2756x^26+3590x^28+2236x^30+1683x^32+626x^34+312x^36+22x^38+32x^40+6x^44

The gray image is a code over GF(2) with n=54, k=14 and d=16.
This code was found by Heurico 1.16 in 6.28 seconds.