The generator matrix

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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+49x^44+10x^46+1x^48+2x^50+1x^52

The gray image is a code over GF(2) with n=352, k=6 and d=176.
This code was found by Heurico 1.16 in 0.0468 seconds.