The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+56x^44+120x^45+254x^46+342x^47+768x^48+842x^49+1223x^50+1034x^51+1344x^52+790x^53+629x^54+344x^55+240x^56+64x^57+52x^58+34x^59+16x^60+6x^61+17x^62+6x^63+7x^64+2x^65+1x^74

The gray image is a code over GF(2) with n=408, k=13 and d=176.
This code was found by Heurico 1.16 in 1.07 seconds.