The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^18+210x^19+441x^20+642x^21+1101x^22+1284x^23+1899x^24+2540x^25+2892x^26+3468x^27+3330x^28+3532x^29+3102x^30+2608x^31+1953x^32+1312x^33+954x^34+594x^35+421x^36+162x^37+141x^38+28x^39+19x^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 1.10 in 14.1 seconds.