The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  0  1  2  2  4  1  2 12  1  1  1  1  2  1  1
 0  2  0  2  0 10 12 14  4  4  6  6 10  2  0  8 14  4  2  0  6  0  6 12 10  4  2  8  0
 0  0  2  2 12 14  6  4  2  4  6  0  6  0  2  0  4  2  2  0  8  2  8  6  6 10 12  4  0
 0  0  0  8  0  0  0  8  8  8  8  8  0  0  8  8  8  0  0  0  0  8  8  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  0  8  8  0  8  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  0  0  8  0  0  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  8  0  8  8  8  8  0  8  0  0  8  0  0  0

generates a code of length 29 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+69x^22+64x^23+373x^24+340x^25+927x^26+2104x^27+2314x^28+4188x^29+2040x^30+2128x^31+1051x^32+332x^33+272x^34+56x^35+94x^36+4x^37+19x^38+7x^40+1x^42

The gray image is a code over GF(2) with n=232, k=14 and d=88.
This code was found by Heurico 1.16 in 1.55 seconds.