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  8  0  0  0  0  0  0  0  0  8  8  0  0  0  8  8  8  8  8  0  0  0  0  0  8  8
 0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  0  8  8  0  0  0  0  0  0  8  8  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  8  0  0  8  8  0  8  8  0  0  8  8  0  0  8  8  8  8  8
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  8  8  0  8  8  0  8  8  8  8  8  8  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  8
 0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  0

generates a code of length 27 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+29x^20+36x^22+95x^24+362x^26+1024x^27+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=216, k=11 and d=80.
This code was found by Heurico 1.16 in 0.0433 seconds.