The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^6+168x^7+414x^8+664x^9+1332x^10+1960x^11+2252x^12+2648x^13+2286x^14+1848x^15+1353x^16+776x^17+388x^18+120x^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 1.10 in 0.228 seconds.