The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+43x^18+30x^19+124x^20+136x^21+295x^22+314x^23+457x^24+624x^25+691x^26+956x^27+872x^28+928x^29+683x^30+612x^31+490x^32+336x^33+289x^34+134x^35+92x^36+24x^37+45x^38+2x^39+11x^40+1x^42+1x^46+1x^48

The gray image is a code over GF(2) with n=56, k=13 and d=18.
This code was found by Heurico 1.16 in 2.15 seconds.