The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  2  1  1  4  1  1  4  2  4  0  2  8  0  1  1
 0  2  0  0  0  2  6 14  0  8 14  6 12 14 10  4 10 10 10 12  0  4  4  4  4  4  2  2 14  2  2  6  4  2  6  8
 0  0  2  0  2  2  2  0  4 14 10  0  8 12 14  2 10 14 12 12  2  6  8 10  2 10 14  8  2 12 12  4  0  2  8  0
 0  0  0  2  2  0  2 10  8  2  0 14 14 12  2  8  4  6 14  0  8 10 14  2 14  4  4 10  0 14 12 12  2 14  0  4
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  8  8  8  8  0
 0  0  0  0  0  8  0  8  8  8  0  0  8  8  8  8  0  8  8  8  8  0  8  0  8  8  8  8  0  8  0  8  8  0  8  0

generates a code of length 36 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+102x^29+391x^30+628x^31+1229x^32+2006x^33+3483x^34+5484x^35+6190x^36+5448x^37+3515x^38+2038x^39+1173x^40+510x^41+351x^42+136x^43+45x^44+30x^45+2x^46+2x^47+1x^48+2x^50+1x^52

The gray image is a code over GF(2) with n=288, k=15 and d=116.
This code was found by Heurico 1.16 in 8.22 seconds.