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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+9x^42+34x^43+173x^44+26x^45+6x^46+2x^47+2x^48+1x^54+2x^61

The gray image is a code over GF(2) with n=352, k=8 and d=168.
This code was found by Heurico 1.16 in 0.0348 seconds.