The generator matrix

 1  0  1  1  1 14  1  0  1 14  1  1  1 14  0  1  1  1  1  1  1  8  8  1 10 12  1  1  2  1  2  2  1  2  1  1
 0  1 11  6  1  1  8  1  3  1  6  5  5  1  1  6 15  8 11  0 11  1  1 14  1  1 13  6  1  6  0 10  9  1 10  0
 0  0 12  0  0  0  0  0  8  8  0 12  4 12 12 12  0 12 12 12  8  4  8  4  4  8  4  0  8  8 12 12 12 12  8 12
 0  0  0 12  0  0  8  4  8  4 12  8 12 12 12  8  4  8  4  4  4  0  0 12  4  0  0  0 12  8  0 12  0  8  8  4
 0  0  0  0  4 12 12 12  8  0  4 12  8 12  8  4  4  0 12  8  8 12 12 12  0  8  0 12 12  0  8  0  4  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+112x^30+108x^31+602x^32+1064x^33+2112x^34+2560x^35+3134x^36+2928x^37+2062x^38+876x^39+524x^40+136x^41+86x^42+8x^43+58x^44+10x^46+1x^48+2x^50

The gray image is a code over GF(2) with n=288, k=14 and d=120.
This code was found by Heurico 1.16 in 1.67 seconds.