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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+38x^42+62x^43+64x^44+106x^45+159x^46+348x^47+511x^48+342x^49+153x^50+120x^51+54x^52+30x^53+32x^54+12x^55+8x^56+2x^57+2x^59+2x^60+1x^62+1x^82

The gray image is a code over GF(2) with n=384, k=11 and d=168.
This code was found by Heurico 1.16 in 0.142 seconds.