The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+83x^46+352x^47+946x^48+1542x^49+2776x^50+3248x^51+5147x^52+4944x^53+5022x^54+3210x^55+2681x^56+1366x^57+728x^58+340x^59+228x^60+84x^61+28x^62+18x^63+18x^64+2x^66+3x^68+1x^70

The gray image is a code over GF(2) with n=424, k=15 and d=184.
This code was found by Heurico 1.16 in 9.79 seconds.