The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  2  8  2  4  2  2  2  2  1  1  1  1  1  1  1  1
 0  2 12  6  8 14  4 10  0  6 12 10  8 14  6  2  4  2 10  2 14  2  2  2  0 12  8  4  0  8 12  4  6 14 10  2

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

Homogenous weight enumerator: w(x)=1x^0+120x^36+6x^40+1x^48

The gray image is a code over GF(2) with n=288, k=7 and d=144.
This code was found by Heurico 1.16 in 0.0136 seconds.