The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+12x^28+3x^32

The gray image is a code over GF(2) with n=54, k=4 and d=28.
This code was found by Heurico 1.16 in 0.00256 seconds.