The generator matrix

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

generates a code of length 19 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+94x^14+192x^16+252x^18+195x^20+184x^22+91x^24+12x^26+1x^28+2x^30

The gray image is a code over GF(2) with n=38, k=10 and d=14.
This code was found by Heurico 1.16 in 0.024 seconds.