The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  4  1  2  4  1  2  4  2  1  1
 0 12  0  0  0  0  0  0  8 12  4  4  8 12  0  4  4 12  4 12  4 12 12  8  4  0  0
 0  0 12  0  0  0  4 12 12  4  4  0  8 12  4  4  8  4 12  0 12  8  4  0 12  0  0
 0  0  0 12  0  4  4 12  0  8  4 12  0  8 12 12  8  8  0  0  8  4  0  4 12  4  0
 0  0  0  0 12  4  0 12  4 12  4  0 12  0  8  0  4  4  4  8  8 12 12  0  4  4  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  0  8  0  0  8  8  0  8  8  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+73x^18+82x^19+228x^20+286x^21+480x^22+728x^23+1359x^24+3270x^25+6033x^26+7570x^27+6066x^28+3378x^29+1394x^30+782x^31+475x^32+210x^33+189x^34+52x^35+58x^36+24x^37+22x^38+2x^39+5x^40+1x^42

The gray image is a code over GF(2) with n=216, k=15 and d=72.
This code was found by Heurico 1.16 in 6.61 seconds.