The generator matrix

 1  0  1  1  1 14  1  1  8  1  6  1  1  1  1  1 14  8 10  4  1  0  1  4 10  1  1  1  1
 0  1 11  6  5  1  0  3  1 14  1 13  7  6  3  8  1  1  1  1  4  2  4  1  1  5  3  8  0
 0  0 12  0  4  0  4  0  4  4  4  8  4  4 12  0 12  0  8  4  4  4  4  4 12  0  0  0  0
 0  0  0 12  4  4  4  0  0  8 12 12  0  4 12  4  0  4  8  0  8 12  0  8  4  0  0  4  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  8  8  8  8  0  0  0  0  8  0

generates a code of length 29 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+20x^20+54x^21+133x^22+274x^23+653x^24+1226x^25+3474x^26+7134x^27+13121x^28+13310x^29+13127x^30+7194x^31+3497x^32+1230x^33+652x^34+234x^35+106x^36+52x^37+19x^38+12x^39+9x^40+2x^42+1x^44+1x^46

The gray image is a code over GF(2) with n=232, k=16 and d=80.
This code was found by Heurico 1.16 in 14.1 seconds.