The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  2  1
 0  1  0  0  1  0  0  1  1  0  0  0  0
 0  0  1  0  1  0  1  0  1  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  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+103x^4+347x^6+128x^7+1514x^8+1280x^9+2565x^10+3968x^11+3662x^12+5632x^13+3662x^14+3968x^15+2565x^16+1280x^17+1514x^18+128x^19+347x^20+103x^22+1x^26

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 1.6 seconds.