The generator matrix

 1  0  1  1  1 14  1  1  0  1  1  2  6  1  1  1 12  1  1  1  1  1  1  4 10  1  1  4  1  1  2  1
 0  1 11 14  5  1  0  3  1  6 13  1  1  4 15  1  1 10 12  2  0  9  4  1  1  3 12  8 14 14 14  6
 0  0 12  4  0  4 12  0 12  8 12  4  0  4  8  4  0  8  0  4  8  8 12  4  0  8  0  4  4 12 12  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  0  0  0  8  8  0  0  8  8  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  0  8  8  0  0  8
 0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  0  0  8  8  0  8  0  0  0  8  0  0  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  8  0  8  8  0  8  8  8  0  0  8  0

generates a code of length 32 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+172x^24+20x^25+390x^26+368x^27+1927x^28+3904x^29+8752x^30+10032x^31+14409x^32+10056x^33+8668x^34+3920x^35+2038x^36+352x^37+352x^38+16x^39+121x^40+4x^41+14x^42+19x^44+1x^56

The gray image is a code over GF(2) with n=256, k=16 and d=96.
This code was found by Heurico 1.16 in 60.7 seconds.