The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^18+94x^19+247x^20+320x^21+513x^22+674x^23+944x^24+1272x^25+1471x^26+1748x^27+1683x^28+1688x^29+1519x^30+1292x^31+1011x^32+744x^33+469x^34+270x^35+197x^36+72x^37+63x^38+18x^39+12x^40+5x^42+1x^44+1x^46

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 15 seconds.