The generator matrix

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

generates a code of length 27 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+12x^26+12x^28+4x^30+3x^32

The gray image is a code over GF(2) with n=54, k=5 and d=26.
This code was found by Heurico 1.16 in 0.00185 seconds.