The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+200x^44+164x^45+1188x^46+1188x^47+2928x^48+3404x^49+5002x^50+4828x^51+4964x^52+3420x^53+2790x^54+1148x^55+986x^56+180x^57+278x^58+4x^59+59x^60+22x^62+13x^64+1x^76

The gray image is a code over GF(2) with n=408, k=15 and d=176.
This code was found by Heurico 1.16 in 10.2 seconds.