The generator matrix

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

generates a code of length 27 over Z8 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+137x^16+138x^18+784x^20+1274x^22+512x^23+3967x^24+2048x^25+5812x^26+3072x^27+6396x^28+2048x^29+3492x^30+512x^31+1722x^32+514x^34+272x^36+34x^38+29x^40+4x^44

The gray image is a code over GF(2) with n=108, k=15 and d=32.
This code was found by Heurico 1.16 in 10 seconds.