The generator matrix

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

generates a code of length 13 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+53x^4+48x^6+340x^8+424x^10+512x^11+1266x^12+3072x^13+936x^14+512x^15+721x^16+120x^18+169x^20+8x^22+10x^24

The gray image is a code over GF(2) with n=52, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0572 seconds.