The generator matrix

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

generates a code of length 27 over Z16 who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+28x^18+205x^20+8x^21+511x^22+112x^23+914x^24+376x^25+1360x^26+9248x^27+1458x^28+376x^29+1022x^30+112x^31+431x^32+8x^33+140x^34+57x^36+11x^38+6x^40

The gray image is a code over GF(2) with n=216, k=14 and d=72.
This code was found by Heurico 1.16 in 1.76 seconds.