The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  1  1  2  8  1  2  1  1  4  8  1  2  2  0  2  8  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10 12 14  2  4 10 12  4  2 14  0  8 12  2  2  8  8 14  0 14  2  8
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4 10  4  2  2  2  0  2 12  2 10 14  4 12  2  6 10  2  2  4 12  4
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  0  0  0  8  0  8  0  8  8  0
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0  8  8  0  8  0  8
 0  0  0  0  0  8  0  8  8  0  8  8  8  0  0  8  8  8  8  8  0  0  0  0  8  0  8  8  8  8  8  8  0  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+48x^30+138x^31+464x^32+602x^33+830x^34+1470x^35+1217x^36+1434x^37+804x^38+544x^39+349x^40+136x^41+102x^42+22x^43+15x^44+2x^45+8x^46+2x^47+2x^48+2x^49

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 0.571 seconds.