The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+106x^34+16x^35+304x^36+176x^37+548x^38+576x^39+731x^40+576x^41+508x^42+176x^43+190x^44+16x^45+108x^46+48x^48+10x^50+5x^52+1x^60

The gray image is a code over GF(2) with n=320, k=12 and d=136.
This code was found by Heurico 1.16 in 0.274 seconds.