The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+285x^38+144x^39+791x^40+384x^41+1051x^42+352x^43+610x^44+128x^45+275x^46+16x^47+35x^48+13x^50+2x^52+8x^54+1x^56

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 1.23 seconds.