The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^6+753x^8+3120x^10+7448x^12+9888x^14+7427x^16+3152x^18+744x^20+104x^22+11x^24

The gray image is a code over GF(2) with n=28, k=15 and d=6.
This code was found by Heurico 1.16 in 5.28 seconds.