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

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

Homogenous weight enumerator: w(x)=1x^0+91x^44+244x^46+572x^48+1166x^50+1215x^52+488x^54+174x^56+72x^58+53x^60+12x^62+4x^64+2x^66+1x^68+1x^80

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 0.422 seconds.