The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  2  2  2  2  2  4  0  1  1  4  0  1  1  4  4  8  8
 0 12  0 12  8  4  8  4  0 12  0 12  8  4 12  8 12  4  4  0  8  4  0  8 12  4  0  8 12  4  0  8  4  4  4  4
 0  0  8  8  8  8  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  0  0  0  0  8  0  0  8  0  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+122x^36+2x^40+2x^44+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 0.0305 seconds.