The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+94x^20+8x^21+208x^22+64x^23+606x^24+504x^25+1699x^26+1920x^27+1621x^28+504x^29+559x^30+64x^31+220x^32+8x^33+89x^34+17x^36+5x^38+1x^40

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 0.479 seconds.