The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  4  1  1 10  1  1  1  1  1 12  2  1  1  1  1  0  1  6  1 10  1  1  1  1  6  6  1  1 14  1  2  4  4  1  4  1  1  1  1
 0  1 11  6 13  1  0  3  1 14  1  5  1 12  7  1  2  9 15  1  4  1  1 14 11  8  5  1 10  1  6  1  9  0  7  2  1  1  9  2  1  2  1  1  2  6  8 10  5  0  0
 0  0 12  0  4  0 12  0  4 12 12  8 12  8  4  0  4  8  8  4  4  0 12  4  4 12  0  0  0  8  0  8  0  0 12  4  8  8  8 12  4 12 12  4 12  0  4  0  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  0  8  8  0  8  8  8  8  0  0  0  8  0  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  8  8  0  0  0  0  0  8  8  8  0  8  8  0  0  0  0  0  8  0  0  8  8  0  8  0  8  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  8  0  8  0  8  8  8  8  0  0  8  8  8  8  0  8  0  8  8  8  0  8  0  8  0  0  0  8  8  0  0  0  0  0  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  8  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  0  0  8
 0  0  0  0  0  0  0  8  8  0  8  8  8  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  8  0  8  0  8  8  0  0  8  8  8  8  0  8  8  8  0  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+38x^42+64x^43+195x^44+276x^45+835x^46+932x^47+3258x^48+2570x^49+6438x^50+3574x^51+6484x^52+2594x^53+3247x^54+974x^55+741x^56+174x^57+174x^58+82x^59+55x^60+18x^61+13x^62+6x^63+15x^64+6x^66+2x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=408, k=15 and d=168.
This code was found by Heurico 1.16 in 9.98 seconds.