The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  0  1  2 12  1  2  0  1  1  2 12  1  1  0  1  1
 0  2 12  6  0  6 12 10  0  6  6  2 12 10  2 10  6  2  6  0 10  2 12 10  2  0  6
 0  0  8  0  0  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  8  0  0  0  8
 0  0  0  8  0  0  0  0  0  8  0  8  0  8  0  8  0  0  8  8  0  0  8  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  8  0  0  8  0  0  0  8  0  0  0  8  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  0  8  8  0  8  0  0  0  8  0
 0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  0  0  8  0  8  8  8
 0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  8  0  0  8  8  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+130x^20+212x^22+192x^23+1108x^24+2304x^25+2100x^26+4224x^27+2240x^28+2304x^29+988x^30+192x^31+311x^32+28x^34+46x^36+4x^40

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 34.9 seconds.