The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+252x^16+410x^20+128x^22+1666x^24+1280x^26+8192x^27+2578x^28+640x^30+835x^32+334x^36+62x^40+6x^44

The gray image is a code over GF(2) with n=108, k=14 and d=32.
This code was found by Heurico 1.16 in 3.23 seconds.