The generator matrix

1 0 0 0 0 0 1 1 1 1 1 1 0 0 2 1 1 1 2 2 2 2 2 1 2 1 1 1
0 1 0 0 0 0 0 0 1 1 3 2 1 0 1 3 3 1 2 1 2 0 0 3 1 0 0 0
0 0 1 0 0 0 0 1 1 2 3 0 1 2 3 1 3 0 1 0 1 2 1 3 3 1 0 0
0 0 0 1 0 0 1 0 0 2 1 3 1 1 1 3 3 3 1 0 2 2 3 0 3 1 0 0
0 0 0 0 1 0 1 0 1 2 2 3 3 3 2 3 0 0 2 1 1 1 1 1 2 0 0 0
0 0 0 0 0 1 1 3 2 1 0 0 1 2 2 0 1 0 3 2 1 3 0 1 2 2 0 0
0 0 0 0 0 0 2 2 0 2 0 0 0 2 2 2 2 2 0 2 0 2 0 2 0 0 0 0

generates a code of length 28 over Z4 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+70x^18+280x^20+630x^22+1022x^24+1298x^26+1484x^28+1462x^30+1038x^32+575x^34+247x^36+55x^38+23x^40+5x^42+1x^44+1x^46

The gray image is a code over GF(2) with n=56, k=13 and d=18.
This code was found by Heurico 1.10 in 0.944 seconds.