The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+97x^6+120x^7+478x^8+664x^9+1284x^10+1912x^11+2252x^12+2776x^13+2206x^14+1960x^15+1289x^16+648x^17+500x^18+104x^19+76x^20+8x^21+9x^22

The gray image is a code over GF(2) with n=26, k=14 and d=6.
This code was found by Heurico 1.16 in 1.78 seconds.