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

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

Homogenous weight enumerator: w(x)=1x^0+146x^42+20x^43+225x^44+64x^45+408x^46+696x^47+1101x^48+656x^49+374x^50+84x^51+132x^52+16x^53+70x^54+66x^56+24x^58+10x^60+2x^62+1x^76

The gray image is a code over GF(2) with n=384, k=12 and d=168.
This code was found by Heurico 1.16 in 0.415 seconds.