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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+318x^32+512x^34+128x^36+64x^40+1x^64

The gray image is a code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 5.57 seconds.