The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  1  4  1  2  1  4  4  1  4  2  2  2  1
 0 12  0  0  0  0  0  0  0  0  0 12 12  4  4  8  4  4  8  4  4  4 12  0  4  4  4  4  8  0 12 12  4  8 12 12  4 12  8  8  4  8  4 12 12  0 12  4  8  0  0
 0  0 12  0  0  0  0  0  0  0  4  0  4  4  4 12  8 12  4  8  8  4  0  4  4  0  8 12  0 12 12  0  8  4  4  4  8 12 12  4  0  4  4  4  8  8 12  8  8  0  0
 0  0  0 12  0  0  0  4 12 12  4 12  0 12  0  0  8  4  8 12  4  4  0  4  8  8 12  4  4 12  0  8  8  0  4 12 12  0 12 12 12  8  8  8  0  0  0  4  8  4  0
 0  0  0  0 12  0  4  4  4  0  8  8  8  0  4 12  4  0  0  0  4 12  8 12  8  4 12  8 12 12 12 12  0  4  0 12  4 12  0 12 12  4  0  8 12 12  4  8  0  0  0
 0  0  0  0  0 12  4  8  4  4  0  0 12 12  4  0  8  8  4 12 12  8  4  0  0  4  0  8 12 12  0  8  0  0  8 12  4  8  4  8 12 12  4 12 12  8  8  0  4  4  0
 0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  0  8  0  8  8  8  0  0  8  8  8  8  0  8  0  8  0  0  0  8  0  8  0  0  8  0  8  0  0  8  8  8  0  0

generates a code of length 51 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+59x^40+86x^41+208x^42+266x^43+319x^44+448x^45+680x^46+874x^47+1647x^48+3274x^49+5297x^50+6466x^51+5304x^52+3358x^53+1630x^54+842x^55+615x^56+416x^57+358x^58+236x^59+161x^60+90x^61+81x^62+20x^63+22x^64+8x^65+1x^66+1x^78

The gray image is a code over GF(2) with n=408, k=15 and d=160.
This code was found by Heurico 1.16 in 19.5 seconds.