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

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

Homogenous weight enumerator: w(x)=1x^0+168x^44+196x^45+653x^46+824x^47+1342x^48+1860x^49+1986x^50+2512x^51+2018x^52+1812x^53+1222x^54+728x^55+558x^56+220x^57+144x^58+32x^59+62x^60+8x^61+21x^62+11x^64+6x^66

The gray image is a code over GF(2) with n=408, k=14 and d=176.
This code was found by Heurico 1.16 in 4.31 seconds.