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  4  1  1  1  1  1  4  1  1
 0 12  0 12  0 12  8  4  0 12  0 12  0  4  8 12  4  8  8 12 12  4  0  0  0  0  8  8  8 12 12  4  4  8  0  0
 0  0  8  0  0  0  8  0  0  0  8  8  0  8  8  0  8  8  0  8  8  8  0  8  0  8  8  0  0  0  8  8  0  0  0  0
 0  0  0  8  0  0  0  8  0  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  8  8  8  0  8  8  0  0  8  0  0  0
 0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0  8  8  8  8  0  8  8  0  8  0  0  8  0  0  8  0  0  0
 0  0  0  0  0  8  0  8  8  8  0  0  8  8  8  0  0  8  8  8  0  8  8  0  0  8  8  0  0  0  8  0  8  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+51x^32+224x^34+555x^36+128x^38+12x^40+32x^42+20x^44+1x^68

The gray image is a code over GF(2) with n=288, k=10 and d=128.
This code was found by Heurico 1.16 in 0.0383 seconds.