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  2  1  1  1  1  1  2  1  1  2  0  2  0
 0  2 12  6  0  6 12 10  0  6 10 12 14  0 10  4  8  6 12  2  6  8 10 12  8  0  8 12  4  6 14  4  2  2  6  2  6  2
 0  0  8  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  8  0  0
 0  0  0  8  0  0  0  8  8  8  8  8  0  8  0  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  8  0  0  8  0  0
 0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  0  0  8  8  8  8  0  0  8  0  0  0  8  0  8  0  0  8  0  0  8  8

generates a code of length 38 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+64x^35+142x^36+128x^37+480x^38+142x^40+64x^43+2x^44+1x^64

The gray image is a code over GF(2) with n=304, k=10 and d=140.
This code was found by Heurico 1.16 in 30 seconds.