The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+79x^4+179x^6+858x^8+512x^9+1173x^10+2048x^11+1806x^12+3072x^13+1806x^14+2048x^15+1173x^16+512x^17+858x^18+179x^20+79x^22+1x^26

The gray image is a code over GF(2) with n=26, k=14 and d=4.
This code was found by Heurico 1.16 in 0.482 seconds.