The generator matrix

 1  0  1  1  1 14  1  1  4  1  1 10  6  1  1 12  1 10 12  1  1  1  2  2  4  2  1  1  1  1  1 14
 0  1  1  0  7  1  2  3  1  6  5  1  1 11  0  1 12  1  1  5 14 11  1  2  1 14 12  5 11  1 12  1
 0  0  2  6  2  4 14  0  2  0  8  6  8  0  4 10 14  2 12 10  8 14 12 10  6  6  4  4  8  0  8  2
 0  0  0 12  0  0 12  0  8  8  8  0  0 12  4 12  8  4 12 12 12  0  8  0  4 12  8 12  4 12  8  0
 0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  0  0  0  8  8  8  0  8  8  0  0  8  8  8

generates a code of length 32 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+186x^27+507x^28+1206x^29+1628x^30+3180x^31+2886x^32+3386x^33+1706x^34+1020x^35+395x^36+202x^37+24x^38+28x^39+17x^40+6x^41+2x^42+2x^43+2x^44

The gray image is a code over GF(2) with n=256, k=14 and d=108.
This code was found by Heurico 1.16 in 67.4 seconds.