The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+34x^7+154x^8+192x^9+300x^10+470x^11+532x^12+644x^13+632x^14+494x^15+309x^16+184x^17+92x^18+26x^19+28x^20+4x^21

The gray image is a code over GF(2) with n=26, k=12 and d=7.
This code was found by Heurico 1.16 in 0.0849 seconds.