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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  2  1  2  1  2  4  1  0  2  2
 0 12  0  0  0  4 12  4  8 12  8  0  0  4  4  4  4 12  8  0 12  8  8  0  8 12  4  0  4  4  0  0  4  0  8  8  8 12 12  4  0  4 12  0  0  4  0 12  8 12  4 12  0
 0  0 12  0  4  4  4  8  0  4  8  4 12  4  8  0  0  0  8 12  0  4 12  4  8  0 12  0 12  4  8  4  4  0  8  8  0 12  0  4  8 12 12 12  8 12 12  0  8  8  4  0  4
 0  0  0 12  4  0  4  4  8  0 12  4  8  4  0  4  4  4  4 12  0 12  8 12  4  0  8  8 12  8  0  0 12  0  0  8  4  0  8  8  4  0  4  8  8  8 12  4 12  4 12  0  4
 0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  0  8  8  8  0  8  8  8  0  0  8  0  8  0  8  8  0  0  0  8  0  0  0  8  0  0  8  0  8  0  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  8  8  8  0  8  8  0  0  8  0  8  8  8  8  0  0  8  8  8  8  0  8  0  8  8  0  8  0  8  0  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+100x^46+8x^47+200x^48+44x^49+207x^50+244x^51+800x^52+936x^53+768x^54+256x^55+215x^56+44x^57+132x^58+4x^59+87x^60+40x^62+8x^64+1x^66+1x^84

The gray image is a code over GF(2) with n=424, k=12 and d=184.
This code was found by Heurico 1.16 in 0.439 seconds.