The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  6  1  1 12  1 10  1  1  1  1  2  2  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  6  1  5 15  1  9  1  0  6  3  3  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  0  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  0  0  0  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  8  0  0  8  0  8  8  8  8  8  0  8  0  8  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  0  0  8  8  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  0  0  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  0  8  0  8  8  8  0  8  0  8  0  8
 0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  0  8  8  0  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+30x^20+14x^21+62x^22+120x^23+156x^24+812x^25+848x^26+6036x^27+3009x^28+10632x^29+3004x^30+6004x^31+824x^32+820x^33+160x^34+124x^35+64x^36+10x^37+22x^38+4x^39+10x^40+1x^44+1x^48

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 3.46 seconds.