The generator matrix

 1  0  1  1  1 10  1  1 14  1  1  6 10  1  1 12  1  1  0  1  8  1 10  1  1  1  1  1 12  2  1  1  2  1  1  8
 0  1  1  0  3  1  8 11  1 10  3  1  1  7  0  1  2  5  1  5  1 14  1 13  4  1  4  7  1 12  6 14  8 12  1  2
 0  0  2  0 14  8  2 12  2 14  4  6  4  2  6 10  4  4  8 10  6  6 14 12  8 10 12  0  6  2  0  6  2  8  4  6
 0  0  0  2 14 14  6  0 14  8  2  0  2  8  4  2 14  4  6  2 12 10  6 14  6  6  4 10 14  2  6  6 14  4  4  2

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

Homogenous weight enumerator: w(x)=1x^0+252x^31+554x^32+1244x^33+1887x^34+3110x^35+2670x^36+2804x^37+1778x^38+1264x^39+399x^40+252x^41+107x^42+30x^43+24x^44+4x^45+4x^46

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 1.53 seconds.