The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^14+98x^15+311x^16+380x^17+702x^18+924x^19+1275x^20+1612x^21+1708x^22+2096x^23+1718x^24+1732x^25+1328x^26+900x^27+706x^28+356x^29+256x^30+78x^31+82x^32+16x^33+18x^34+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 10.1 seconds.