The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+12x^42+96x^43+12x^44+2x^46+3x^48+2x^54

The gray image is a code over GF(2) with n=344, k=7 and d=168.
This code was found by Heurico 1.16 in 0.0409 seconds.