The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^18+88x^19+232x^20+336x^21+552x^22+678x^23+983x^24+1258x^25+1377x^26+1696x^27+1716x^28+1744x^29+1548x^30+1340x^31+957x^32+676x^33+502x^34+280x^35+188x^36+80x^37+68x^38+14x^39+19x^40+2x^41+1x^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 16.4 seconds.