The generator matrix

 1  0  1  1  1  6  1 12  1  1 14  1  1  1 10  1  8  1  1  1  1  1  2  1  1  1  8  1 12  1  4  4  1  1  1  1
 0  1 11  6 13  1 12  1  3 10  1  1  7  8  1 14  1 13 15  4  0  2  1  6  3 12  2 11  1  2  1  8 12  5  7  0
 0  0 12  0  4  0  0  8  0  8 12 12  4  4  8 12  4 12  8  4  8 12  4  0  8  0  4 12  0  4  4  4  0  0 12  0
 0  0  0  8  0  0  8  0  0  0  0  0  8  8  8  0  8  8  8  8  0  8  0  8  0  0  8  8  8  0  0  0  8  0  0  0
 0  0  0  0  8  0  8  8  8  0  8  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0  0  0  8  0  0  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  8  8  0  8  0  0  8  8  0  8  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  0

generates a code of length 36 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+36x^30+116x^31+330x^32+506x^33+1107x^34+1190x^35+1681x^36+1174x^37+1119x^38+466x^39+277x^40+110x^41+30x^42+18x^43+15x^44+2x^45+8x^46+2x^47+3x^50+1x^54

The gray image is a code over GF(2) with n=288, k=13 and d=120.
This code was found by Heurico 1.16 in 0.42 seconds.