The generator matrix

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

generates a code of length 28 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+18x^26+28x^28+12x^30+3x^32+2x^42

The gray image is a code over GF(2) with n=56, k=6 and d=26.
This code was found by Heurico 1.16 in 0.209 seconds.