The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+392x^34+120x^35+541x^36+656x^37+782x^38+640x^39+494x^40+112x^41+240x^42+8x^43+83x^44+22x^46+4x^50+1x^56

The gray image is a code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 75.5 seconds.