The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  1  1  2  2  1  1  0  1  1  0  1  1  2  1  2
 0  2 12  6  0  6 12 10  0  6  6  2 12 10 10  2  0  6 10  6 10 12  6  2  0 14  2 12  6  6  6  6
 0  0  8  0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  8  0  0  8  8  8  0  8
 0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  0  0  0  8  8  0  8  8  8  8  0  8  8  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  0  8  8  8  8  8  0  0  0  0  8  0  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  0  0  0  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  8  0  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+96x^24+128x^26+64x^27+775x^28+576x^29+2304x^30+2432x^31+3650x^32+2432x^33+2304x^34+576x^35+758x^36+64x^37+128x^38+74x^40+19x^44+3x^48

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 2.05 seconds.