The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+85x^14+132x^15+356x^16+356x^17+579x^18+960x^19+1237x^20+1632x^21+1802x^22+1992x^23+1769x^24+1704x^25+1374x^26+928x^27+666x^28+384x^29+241x^30+84x^31+65x^32+20x^33+15x^34+1x^36+1x^40

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 9.18 seconds.