The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  1  1  1  0  0  1  2  0  2  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  2  3  3  3  1  3  2  1  3  0  1  2  2  1  2
 0  0  1  0  0  0  0  0  0  3  2  1  3  1  3  3  1  2  2  1  2  1  1  0  1  0  2  2
 0  0  0  1  0  0  0  0  3  1  2  2  1  1  2  3  2  1  2  2  0  2  1  2  1  0  1  1
 0  0  0  0  1  0  0  0  1  0  3  3  2  3  0  3  1  2  1  2  0  0  1  0  1  3  1  1
 0  0  0  0  0  1  0  1  0  3  1  2  1  0  1  2  3  0  0  3  3  2  0  0  0  2  1  2
 0  0  0  0  0  0  1  1  3  2  2  1  1  2  0  3  3  3  1  3  0  3  2  1  1  3  0  3
 0  0  0  0  0  0  0  2  2  0  0  2  2  0  0  2  2  2  0  0  2  0  2  0  0  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+138x^18+210x^19+439x^20+642x^21+1051x^22+1284x^23+1925x^24+2540x^25+2936x^26+3468x^27+3322x^28+3532x^29+3054x^30+2608x^31+1969x^32+1312x^33+994x^34+594x^35+383x^36+162x^37+143x^38+28x^39+25x^40+4x^41+4x^42

The gray image is a code over GF(2) with n=56, k=15 and d=18.
This code was found by Heurico 1.16 in 43.2 seconds.