The generator matrix

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

generates a code of length 13 over Z4 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+32x^5+128x^6+322x^7+759x^8+1528x^9+2568x^10+3784x^11+4736x^12+5064x^13+4728x^14+3756x^15+2583x^16+1544x^17+760x^18+328x^19+112x^20+24x^21+8x^22+2x^23+1x^24

The gray image is a code over GF(2) with n=26, k=15 and d=5.
This code was found by Heurico 1.16 in 3.01 seconds.