The generator matrix

 1  0  1  1  1  0  1  1  4  1  1  2  1
 0  1  1  0  1  1  0  7  1  0  0  4  0
 0  0  2  0  0  0  0  0  2  2  6  4  0
 0  0  0  2  0  0  0  4  2  2  4  6  0
 0  0  0  0  2  0  0  6  0  4  6  2  2
 0  0  0  0  0  2  0  2  4  4  6  6  4
 0  0  0  0  0  0  2  2  6  0  6  4  6

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

Homogenous weight enumerator: w(x)=1x^0+87x^6+156x^7+536x^8+1232x^9+3206x^10+7492x^11+12606x^12+15016x^13+12436x^14+7460x^15+3287x^16+1280x^17+522x^18+124x^19+82x^20+8x^21+5x^22

The gray image is a code over GF(2) with n=52, k=16 and d=12.
This code was found by Heurico 1.16 in 3.92 seconds.