The generator matrix

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

generates a code of length 13 over Z8 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+84x^6+54x^7+323x^8+350x^9+683x^10+1454x^11+3001x^12+4454x^13+3011x^14+1506x^15+688x^16+314x^17+313x^18+58x^19+83x^20+2x^21+5x^22

The gray image is a code over GF(2) with n=52, k=14 and d=12.
This code was found by Heurico 1.16 in 0.409 seconds.