The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^24+144x^25+297x^26+680x^27+1480x^28+3712x^29+7253x^30+11854x^31+14542x^32+11856x^33+7281x^34+3710x^35+1475x^36+656x^37+254x^38+138x^39+85x^40+16x^41+18x^42+2x^43+1x^44+1x^54

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 19.1 seconds.