The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  1  2
 0 12  0  0  0  0  0  0  0 12  4 12 12  8  8  0 12 12  8  4  8  4  0  8  0  4  8
 0  0 12  0  0  0  4 12  4  4  4  8  0  8 12  8 12 12 12  8  8 12 12 12  8  8  4
 0  0  0 12  0  4  4  4  8  4  0 12  4  8  8  0  8  0  0 12  4  0 12 12 12  8  8
 0  0  0  0 12  4  0  4  4  8  0  8 12  0  8 12 12  0 12  0  8 12 12  8  4 12  8
 0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  8  0  0  0  8  0  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+192x^20+428x^22+731x^24+384x^25+3724x^26+5376x^27+3876x^28+384x^29+676x^30+418x^32+164x^34+28x^36+1x^40+1x^48

The gray image is a code over GF(2) with n=216, k=14 and d=80.
This code was found by Heurico 1.16 in 2.23 seconds.