The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^44+80x^45+121x^46+170x^47+169x^48+650x^49+208x^50+1320x^51+211x^52+640x^53+141x^54+124x^55+68x^56+38x^57+32x^58+32x^59+24x^60+12x^61+8x^62+2x^63+4x^64+4x^65+2x^66+1x^76

The gray image is a code over GF(2) with n=408, k=12 and d=176.
This code was found by Heurico 1.16 in 0.388 seconds.