The generator matrix

 1  1  1  1  2  2  1  1  1  1  1  1  2
 0  2  0  6  2  2  0  0  0  0  0  0  0
 0  0  4  0  0  0  0  0  0  0  0  0  4
 0  0  0  4  0  0  0  0  0  0  0  0  4
 0  0  0  0  4  0  0  0  0  0  0  0  4
 0  0  0  0  0  4  0  0  0  0  0  0  4
 0  0  0  0  0  0  4  0  0  0  0  0  4
 0  0  0  0  0  0  0  4  0  0  0  0  4
 0  0  0  0  0  0  0  0  4  0  0  0  4
 0  0  0  0  0  0  0  0  0  4  0  0  4
 0  0  0  0  0  0  0  0  0  0  4  0  4
 0  0  0  0  0  0  0  0  0  0  0  4  4

generates a code of length 13 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+86x^4+72x^6+1003x^8+1696x^10+2048x^11+5796x^12+12288x^13+4080x^14+2048x^15+2983x^16+288x^18+358x^20+8x^22+13x^24

The gray image is a code over GF(2) with n=52, k=15 and d=8.
This code was found by Heurico 1.16 in 0.885 seconds.