The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  0 12  1  1  2  8  1  0  1  2  1  0  1  1  1  2  8  0
 0  2  0  2  0  0 14  4  6 14  4  2 12  6 12  2  2  6  2  2 12 12  6  2  6  2 14 14 14  2  4  4 12 14  4  2
 0  0  2  2 12  6  6  4  0  4 10  6  8  2 14  4  2  0  0  6  2  4  4  8 14  2  0 14 10 12 14 10  0  4  2  4
 0  0  0  4  0  0  4  0  0  8  8 12  0 12  8  8  0  0  8  8  4 12 12 12  8 12  4 12  0 12  4 12 12  8  0 12
 0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  8  0  0  8  0  8  0  8  8  8  8  8  8  0  0  8  8  8
 0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  8  8  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+206x^30+368x^31+648x^32+1200x^33+1616x^34+2976x^35+2294x^36+3136x^37+1600x^38+1232x^39+548x^40+272x^41+204x^42+32x^43+26x^44+18x^46+3x^48+4x^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 3.16 seconds.