The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+138x^34+448x^35+336x^36+384x^37+208x^38+320x^39+115x^40+64x^41+10x^42+18x^44+4x^46+2x^48

The gray image is a code over GF(2) with n=296, k=11 and d=136.
This code was found by Heurico 1.16 in 0.0423 seconds.