The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+141x^30+108x^31+613x^32+1064x^33+2061x^34+2644x^35+3140x^36+2704x^37+2022x^38+1076x^39+560x^40+72x^41+106x^42+12x^43+36x^44+21x^46+2x^48+1x^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 51.9 seconds.