The generator matrix
1 1 1 1 1 1 1 1 2 1 1 2 1
0 2 0 0 0 0 0 0 6 4 6 2 0
0 0 2 0 0 0 0 4 6 6 4 6 0
0 0 0 2 0 0 0 6 4 2 0 6 0
0 0 0 0 2 0 0 2 0 4 6 6 0
0 0 0 0 0 2 0 2 4 4 4 4 2
0 0 0 0 0 0 2 2 6 0 2 4 2
generates a code of length 13 over Z8 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+95x^6+168x^7+414x^8+664x^9+1236x^10+2984x^11+6460x^12+8792x^13+6410x^14+2872x^15+1257x^16+776x^17+436x^18+120x^19+60x^20+8x^21+15x^22
The gray image is a code over GF(2) with n=52, k=15 and d=12.
This code was found by Heurico 1.16 in 1.55 seconds.