The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+44x^42+82x^43+139x^44+316x^45+403x^46+658x^47+1107x^48+1764x^49+2369x^50+2560x^51+2490x^52+1764x^53+1141x^54+712x^55+296x^56+220x^57+117x^58+78x^59+49x^60+32x^61+15x^62+6x^63+12x^64+5x^66+2x^68+1x^70+1x^74

The gray image is a code over GF(2) with n=408, k=14 and d=168.
This code was found by Heurico 1.16 in 4.33 seconds.