The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^14+112x^15+325x^16+424x^17+678x^18+900x^19+1261x^20+1604x^21+1736x^22+2052x^23+1774x^24+1684x^25+1372x^26+940x^27+642x^28+364x^29+236x^30+92x^31+92x^32+20x^33+14x^34+1x^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.