The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+39x^22+68x^23+114x^24+128x^25+329x^26+864x^27+1089x^28+790x^29+347x^30+124x^31+67x^32+52x^33+49x^34+16x^35+9x^36+6x^37+3x^38+1x^46

The gray image is a code over GF(2) with n=224, k=12 and d=88.
This code was found by Heurico 1.16 in 0.154 seconds.