The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+117x^4+672x^6+2692x^8+5112x^10+7874x^12+7544x^14+5409x^16+2472x^18+793x^20+72x^22+10x^24

The gray image is a code over GF(2) with n=26, k=15 and d=4.
This code was found by Heurico 1.16 in 1.63 seconds.