The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+69x^14+124x^15+95x^16+94x^18+268x^19+94x^20+88x^22+116x^23+64x^24+2x^26+4x^27+2x^28+3x^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 42.3 seconds.