The generator matrix

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

generates a code of length 27 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+29x^20+36x^22+95x^24+362x^26+338x^28+98x^30+39x^32+14x^34+7x^36+2x^38+1x^40+2x^44

The gray image is a code over GF(2) with n=108, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0277 seconds.