The generator matrix

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

generates a code of length 14 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+79x^6+60x^7+359x^8+312x^9+997x^10+1256x^11+1704x^12+2488x^13+1926x^14+2432x^15+1663x^16+1256x^17+1034x^18+344x^19+360x^20+40x^21+59x^22+4x^23+9x^24+1x^26

The gray image is a code over GF(2) with n=28, k=14 and d=6.
This code was found by Heurico 1.16 in 1.58 seconds.