The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^20+76x^21+230x^22+336x^23+560x^24+776x^25+1459x^26+3146x^27+5845x^28+7686x^29+5901x^30+3178x^31+1505x^32+846x^33+544x^34+238x^35+209x^36+86x^37+50x^38+14x^39+6x^40+2x^41+5x^42+1x^44+3x^46

The gray image is a code over GF(2) with n=232, k=15 and d=80.
This code was found by Heurico 1.16 in 7.69 seconds.