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

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

Homogenous weight enumerator: w(x)=1x^0+39x^34+114x^36+64x^37+636x^38+64x^39+52x^40+23x^42+24x^44+6x^46+1x^72

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 0.0652 seconds.