The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+118x^20+16x^21+210x^22+160x^23+518x^24+1008x^25+698x^26+2752x^27+719x^28+1008x^29+438x^30+160x^31+277x^32+16x^33+62x^34+26x^36+4x^40+1x^44

The gray image is a code over GF(2) with n=216, k=13 and d=80.
This code was found by Heurico 1.16 in 0.591 seconds.