The generator matrix

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

generates a code of length 46 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+62x^39+468x^40+1524x^41+2673x^42+5088x^43+7117x^44+9906x^45+11542x^46+10334x^47+7642x^48+4782x^49+2301x^50+1308x^51+412x^52+246x^53+92x^54+24x^55+7x^56+6x^57+1x^60

The gray image is a code over GF(2) with n=368, k=16 and d=156.
This code was found by Heurico 1.16 in 24.8 seconds.