The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+25x^6+113x^8+322x^10+562x^12+564x^14+325x^16+110x^18+22x^20+3x^22+1x^24

The gray image is a code over GF(2) with n=26, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0121 seconds.