The generator matrix

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

generates a code of length 36 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+91x^32+160x^33+67x^34+384x^35+1024x^36+128x^39+36x^40+96x^41+60x^42+1x^66

The gray image is a code over GF(2) with n=288, k=11 and d=128.
This code was found by Heurico 1.16 in 0.0785 seconds.