The generator matrix

 1  0  1  1  1  0  1  0  1  1  1  2  1
 0  1  1  0  1  1  0  1  3  2  0  0  0
 0  0  2  0  0  0  0  2  4  6  0  2  0
 0  0  0  2  0  0  0  2  6  4  6  0  0
 0  0  0  0  2  0  0  2  2  2  2  2  0
 0  0  0  0  0  2  6  2  0  2  4  0  0
 0  0  0  0  0  0  4  0  4  0  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+83x^6+84x^7+412x^8+636x^9+1968x^10+3620x^11+5694x^12+7692x^13+5802x^14+3644x^15+1931x^16+628x^17+400x^18+76x^19+90x^20+4x^21+3x^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 1.04 seconds.