The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^20+32x^21+128x^22+176x^23+323x^24+538x^25+827x^26+1608x^27+2794x^28+3472x^29+2750x^30+1640x^31+837x^32+532x^33+346x^34+152x^35+95x^36+32x^37+40x^38+8x^39+7x^40+2x^41+3x^42+2x^46

The gray image is a code over GF(2) with n=232, k=14 and d=80.
This code was found by Heurico 1.16 in 2.02 seconds.