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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+57x^34+16x^35+50x^36+240x^37+307x^38+240x^39+39x^40+16x^41+47x^42+5x^44+5x^46+1x^68

The gray image is a code over GF(2) with n=304, k=10 and d=136.
This code was found by Heurico 1.16 in 2 seconds.