The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+131x^6+64x^7+484x^8+632x^9+1640x^10+2648x^11+3592x^12+4984x^13+4598x^14+4760x^15+3649x^16+2472x^17+1744x^18+712x^19+464x^20+104x^21+79x^22+8x^23+2x^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 3.9 seconds.