The generator matrix

 1  0  1  1  1  4  1  2  1  1  1 14  0  1  1  1  1  4  1  1 12  1  1  1 10  1  2  1  2 12  1  1  2  8 10  1
 0  1  1  0  3  1 15  1  6  5  2  1  1  8 11 10 11  1  9  2  1  8  3  8  1 13  2  7  1  2 13 14 12 12  1  1
 0  0  2  6  0  2  6  2  0  8  6 12 12  4  4  2  2  4 10  4  2 10 12  8  6  8  6 14  8 14  4  0 10  2 12  6
 0  0  0 12  0  0  8  8  0  0  4  0  0  8  8  4  0  0 12  8  4  8 12  4  0 12  4  4  4  0 12  4  4  8 12  4
 0  0  0  0  8  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  8  8  8  0  8  8  0  8  0  0  8  0  8  0  0  8
 0  0  0  0  0  8  8  0  8  8  8  8  0  0  8  0  0  0  8  8  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+230x^30+308x^31+1543x^32+2056x^33+4067x^34+4720x^35+6736x^36+4964x^37+4246x^38+2004x^39+1320x^40+272x^41+212x^42+8x^43+56x^44+4x^45+12x^46+8x^48+1x^50

The gray image is a code over GF(2) with n=288, k=15 and d=120.
This code was found by Heurico 1.16 in 9.36 seconds.