The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^6+180x^7+426x^8+644x^9+1248x^10+1940x^11+2344x^12+2692x^13+2310x^14+1852x^15+1261x^16+748x^17+440x^18+124x^19+64x^20+12x^21+11x^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 1.9 seconds.