The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^24+138x^25+183x^26+274x^27+305x^28+552x^29+1342x^30+3128x^31+4413x^32+3136x^33+1392x^34+592x^35+299x^36+240x^37+138x^38+96x^39+49x^40+30x^41+17x^42+6x^43+3x^44+1x^52

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 2.69 seconds.