The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1  1  1  0  1 10 12  1  1  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1 12 15 10  1  9  1  2  3  5  0  5  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  0  0  0  8  8  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  0  0  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  0  8  0  8  0  0  0  8  0  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  8  8  0  0  0
 0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  0  0  0  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+49x^24+16x^25+76x^26+224x^27+370x^28+1024x^29+2290x^30+2064x^31+4169x^32+2064x^33+2298x^34+1024x^35+347x^36+224x^37+70x^38+16x^39+43x^40+2x^42+10x^44+2x^48+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 1.19 seconds.