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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+108x^48+4x^49+139x^50+128x^51+416x^52+504x^53+432x^54+128x^55+79x^56+4x^57+45x^58+29x^60+22x^62+6x^64+2x^66+1x^92

The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.199 seconds.