The generator matrix

 1  0  0  1  1  1  2  0  1  4  1  0  0
 0  1  0  1  0  3  1  2  0  1  2  0  1
 0  0  1  1  1  0  1  1  0  2  1  1  1
 0  0  0  2  0  6  0  0  2  2  2  2  4
 0  0  0  0  2  0  0  2  2  6  6  6  6
 0  0  0  0  0  4  0  4  0  0  4  4  4
 0  0  0  0  0  0  4  0  0  4  4  0  4

generates a code of length 13 over Z8 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+48x^7+183x^8+652x^9+1676x^10+3752x^11+6316x^12+7468x^13+6360x^14+3776x^15+1679x^16+644x^17+156x^18+40x^19+12x^20+4x^21+1x^24

The gray image is a code over GF(2) with n=52, k=15 and d=14.
This code was found by Heurico 1.16 in 5.88 seconds.