The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  8  0  2  1  1  1  1  1  0  2  1  2  1  2  1  1  4  1  1
 0  2  0  6  0  6  0  2  4 10  8 14  6  2  2  6 12  2  2 12 10  2 14  8  2  4 10  8  6  0  8  0
 0  0 12  0  0  4  4  4 12  4  8  4  4  8  4  8  8  0  4 12  8  0 12  4  4  0 12  4  0 12  4  0
 0  0  0 12 12  4  4  0  8 12 12  0  4 12  4  0  8 12  4  4  8  8  0  8  0  8  4  8  4  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  0  8  0  8  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  8  0
 0  0  0  0  0  0  8  8  8  8  0  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+32x^24+56x^25+181x^26+250x^27+440x^28+1130x^29+1796x^30+2648x^31+3324x^32+2714x^33+1741x^34+1076x^35+509x^36+254x^37+103x^38+56x^39+39x^40+6x^41+18x^42+2x^43+7x^44+1x^46

The gray image is a code over GF(2) with n=256, k=14 and d=96.
This code was found by Heurico 1.16 in 2.06 seconds.