The generator matrix

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

generates a code of length 23 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+106x^14+132x^15+395x^16+380x^17+726x^18+892x^19+1262x^20+1686x^21+1553x^22+1994x^23+1694x^24+1678x^25+1228x^26+970x^27+776x^28+338x^29+332x^30+106x^31+94x^32+14x^33+22x^34+2x^35+2x^36+1x^38

The gray image is a code over GF(2) with n=46, k=14 and d=14.
This code was found by Heurico 1.10 in 2.41 seconds.