The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^16+251x^18+726x^20+1700x^22+384x^23+3677x^24+1536x^25+5838x^26+4352x^27+5897x^28+1536x^29+3789x^30+384x^31+1691x^32+647x^34+240x^36+62x^38+9x^40+1x^44+1x^46

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 10.7 seconds.