The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^14+116x^15+358x^16+392x^17+713x^18+948x^19+1225x^20+1622x^21+1738x^22+1986x^23+1546x^24+1702x^25+1216x^26+946x^27+852x^28+370x^29+276x^30+98x^31+111x^32+10x^33+23x^34+2x^35+3x^36

The gray image is a code over GF(2) with n=46, k=14 and d=14.
This code was found by Heurico 1.16 in 11.8 seconds.