The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1 12  1  1  1 10  4  1  1  1  1  2  0  6  4  2  0  6  0  4  2  2  1  1  1  1
 0  1 11  6  5  1  9  8  1  7 14  1  4  1 13 10  3  1  1 12 15  2  1  1  1  1  1  1  1  1  0  1  1  6  3  9  7 13
 0  0 12  0  8  0  8  4 12  4 12  4  4  0 12  8  0  8 12  8  0 12  4  4  8  8  4  4  8  0  4 12 12  8  0  0 12 12
 0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  0  0  8  0  8  8  0  8  0  8  8  0  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+236x^35+332x^36+296x^37+376x^38+328x^39+289x^40+88x^41+24x^42+72x^43+1x^48+4x^51+1x^56

The gray image is a code over GF(2) with n=304, k=11 and d=140.
This code was found by Heurico 1.16 in 43.6 seconds.