The generator matrix

 1  0  0  1  1  1  0  1  1  0  1  1  1
 0  1  0  1  0  1  1  0  0  2  1  1  1
 0  0  1  1  1  0  1  0  1  1  1  1  1
 0  0  0  2  0  0  0  0  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  2  0  2  2
 0  0  0  0  0  2  0  0  0  0  2  0  2
 0  0  0  0  0  0  2  0  0  0  2  2  0
 0  0  0  0  0  0  0  2  0  2  0  0  2
 0  0  0  0  0  0  0  0  2  2  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+34x^6+139x^8+192x^9+324x^10+384x^11+516x^12+896x^13+536x^14+384x^15+339x^16+192x^17+124x^18+28x^20+6x^22+1x^24

The gray image is a code over GF(2) with n=26, k=12 and d=6.
This code was found by Heurico 1.16 in 0.154 seconds.