The generator matrix

 1  0  0  1  1  1 10  1 14  1  1  6  1  1 10  6  4  1 12  1  1  1  1 12 12  1  1  1 10  1  1  1  1 12  1  1
 0  1  0  4  5  1  1 14  1  3  8  0  4 15  1  1 14 11  1 15 10  8 15  6  1 13  7  5  1 12  2  0  2  1 12  0
 0  0  1  7  3  4  3  7 10 11  2  1  1 14  5  0  1  4  3  5  0  4  3  1  6  7  1  6 13 14 12 15  5 15  5  0
 0  0  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  0  0  8  8  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  8  8  8  0  0  0  0  8  8  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+102x^31+509x^32+1398x^33+2062x^34+2652x^35+3113x^36+2690x^37+1973x^38+1106x^39+496x^40+196x^41+24x^42+40x^43+9x^44+2x^45+5x^46+4x^47+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 1.19 seconds.