The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+265x^6+1494x^8+5140x^10+9588x^12+9230x^14+5329x^16+1476x^18+228x^20+17x^22

The gray image is a code over GF(2) with n=26, k=15 and d=6.
This code was found by Heurico 1.10 in 2.95 seconds.