The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  1
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  8  8  0  0  8
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  8  8
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  0  8  8  0  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  0  0  8  8  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  0  0  8  8  0  8
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  8  0  0  8  8  8  8  0  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  0  8
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  8  0  0  0  0  0  8  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+100x^20+193x^24+192x^26+3072x^27+312x^28+64x^30+122x^32+36x^36+3x^40+1x^48

The gray image is a code over GF(2) with n=216, k=12 and d=80.
This code was found by Heurico 1.16 in 1.51 seconds.