The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+119x^30+136x^31+505x^32+904x^33+2244x^34+2800x^35+3083x^36+2800x^37+2112x^38+904x^39+493x^40+136x^41+88x^42+37x^44+13x^46+9x^48

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 1.7 seconds.