The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^18+134x^19+224x^20+414x^21+542x^22+756x^23+943x^24+1166x^25+1471x^26+1538x^27+1696x^28+1670x^29+1476x^30+1294x^31+1017x^32+758x^33+488x^34+336x^35+200x^36+84x^37+54x^38+38x^39+15x^40+4x^41+7x^42

The gray image is a code over GF(2) with n=56, k=14 and d=18.
This code was found by Heurico 1.16 in 16.8 seconds.