The generator matrix

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

generates a code of length 17 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+34x^14+72x^15+43x^16+20x^18+48x^19+12x^20+10x^22+8x^23+8x^24

The gray image is a code over GF(2) with n=34, k=8 and d=14.
This code was found by Heurico 1.16 in 0.00381 seconds.