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  0  1  1 12  1  0  2  1  2  1  1  2  1  1  1  1  4  1  1 12  1  1  2  1  1  0  1 12  1
 0  2  0  2  8  0  6 14  0  8  6  2  0 10  0 14 10  4 10  4  2 14 12  4  2  2  4  8  8  2 10  4  4 14  6 14  6  0  4  6  8 10  4  2 12 10  0  0 10  2 10  2  4
 0  0  2  2  0 14  6  8  4 10  2  8  4 14 14 12 12  6 14 12 12  2  8 14  0  8  6  2  6  2  8  4 14 14  2  8 14  8  8 12  2  6  4 12  8 10 14  4  6  4  6  6  2
 0  0  0  4  4  4  0  4 12  4  8  4  0  4  8  8 12 12  8 12  8  4  8  8  8  8  4  8  0  4  0  4  0  4  0 12 12  8  4  0  4 12  8  4  4  0  4  8  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+135x^48+196x^49+392x^50+360x^51+834x^52+440x^53+738x^54+400x^55+284x^56+80x^57+108x^58+52x^59+32x^60+4x^61+24x^62+4x^63+8x^64+1x^68+2x^70+1x^84

The gray image is a code over GF(2) with n=424, k=12 and d=192.
This code was found by Heurico 1.16 in 0.423 seconds.