The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+416x^38+80x^39+707x^40+432x^41+945x^42+432x^43+647x^44+80x^45+209x^46+111x^48+27x^50+5x^52+3x^54+1x^64

The gray image is a code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 66.2 seconds.