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  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  2  1  2  2  1  1  1  1
 0  8  0  0  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  0  0  0  8  0  8  0  8  8  0  8  0  0  8  0  0  8  8  8  8  8  0  0  8  8  0  0  8  8  8  0
 0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  0  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  0
 0  0  0  8  0  0  0  0  8  0  0  8  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  0  8  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  8  0  0  0  8  0
 0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  8  0  0  0  8  0  8  0  0  0  0  0  8  8  0  0  8  0  8  8  8  0  8  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  8  0  8  0  0  8  8  8  0  0  8  8  0  0  0  8  8  8  8  0  0  8  0  8  8  0  0  8  8  8  0  0  0  8  0  8  8  8  0  8  8  0  8  8  8
 0  0  0  0  0  0  8  0  8  8  0  0  0  8  8  0  8  8  8  0  0  0  8  8  0  0  0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  8  0  8  0  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  0  0  0  0  0  8  8  0  8  8  0  0  0  8  8  8  8  8  0  0  0  8  8  0  8  0  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+50x^46+70x^48+40x^50+80x^52+1536x^53+126x^54+88x^56+8x^58+30x^62+16x^64+2x^70+1x^96

The gray image is a code over GF(2) with n=424, k=11 and d=184.
This code was found by Heurico 1.16 in 3.62 seconds.