The generator matrix

 1  0  0  1  1  1  6  1  1  1  1 12  2 14 12  1  6  1  4  2  1  1  8  1  1  1  1 12  1  1 12 14  1  1 14  1
 0  1  0  2  9  3  1 14  5  8  3  1  1  0  1 11  1  4  1 10 11  4  1 13 10 14 13  1 12 10  0  1  4  2  1  0
 0  0  1  1  1  0  1  6  2 15 11  3  6  1  6  6  3 14  5  1 13  3  0  1 11 12  8 13  5 15  1  3  9  4  1  0
 0  0  0  4 12  8  4 12  4  8  0  0 12 12  8  8  8  4 12 12  4 12  4  8  8  4 12  4 12 12 12 12  0  0  0  8

generates a code of length 36 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+84x^31+595x^32+1280x^33+2044x^34+2758x^35+3067x^36+2820x^37+1834x^38+1060x^39+555x^40+166x^41+84x^42+18x^43+5x^44+4x^45+6x^46+1x^48+2x^49

The gray image is a code over GF(2) with n=288, k=14 and d=124.
This code was found by Heurico 1.16 in 1.34 seconds.