The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1  2  1  2  1  2  2  1  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  0  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  0  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  2  2  0  2  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  2  0  0  2
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  0  2  2  2  2  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0  0  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  0  2  0  2  0  2  0  0  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+216x^16+462x^20+224x^22+1694x^24+1120x^26+2438x^28+672x^30+983x^32+32x^34+298x^36+50x^40+2x^44

The gray image is a code over GF(2) with n=54, k=13 and d=16.
This code was found by Heurico 1.16 in 4.52 seconds.