The generator matrix

 1  0  1  1  1  4  1 10  1  6  1  1  1 10  2  1  6  1  1  6  2  1 14  1  1  1  1  1  1
 0  1  1  0 11  1  6  1 13  1  7  2  1  1 10  4  1 12  7  1  6  4  1  4 15  0  7 10  0
 0  0  2  6  0  2  0  2  4  4  6  2  6  2  6  8  8  2 12 12  2  0 14  4  4 14 10  0  0
 0  0  0 12  0  4  4  8 12  4 12 12  0  4  4  4 12  0  0  4  8  8  4  8 12  8  4 12 12
 0  0  0  0 12  4  4 12  4  8  0 12 12  8  4  0  4 12  8 12  4 12  0  4  0  0  4  4 12
 0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  0  0  8  0  8  8  8  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+72x^22+228x^23+634x^24+1680x^25+3242x^26+7468x^27+12410x^28+13976x^29+12520x^30+7580x^31+3189x^32+1600x^33+597x^34+212x^35+86x^36+24x^37+16x^38+1x^50

The gray image is a code over GF(2) with n=232, k=16 and d=88.
This code was found by Heurico 1.16 in 16 seconds.