The generator matrix

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

generates a code of length 32 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+88x^26+8x^27+182x^28+40x^29+330x^30+720x^31+1423x^32+720x^33+270x^34+40x^35+153x^36+8x^37+70x^38+32x^40+10x^42+1x^52

The gray image is a code over GF(2) with n=256, k=12 and d=104.
This code was found by Heurico 1.16 in 0.362 seconds.