The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^39+301x^40+816x^41+1432x^42+2504x^43+3789x^44+4938x^45+5473x^46+4700x^47+3646x^48+2552x^49+1408x^50+616x^51+248x^52+154x^53+65x^54+42x^55+14x^56+4x^57+6x^58+1x^60

The gray image is a code over GF(2) with n=368, k=15 and d=156.
This code was found by Heurico 1.16 in 8.12 seconds.