The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2 12  1  1  2  0  1  2  1  0  2  1  2  0  1  0  1  1  2  1  2  1  4  1
 0  2  0  2  0  8  2 10  8  2 12 14  0 10  4  6  2  2  8 12 14  2  2  0  2 12 10 14  0  4 12  2  8  6  4 14  2 14  2  0
 0  0  2  2 12 14  6 12  0  2 10 12  4 14 14  8  6  6  0  6  2  0  8  6  0  2 14  2  2  2  8  0  6  4 10 12  8  6  6  0
 0  0  0  4  0  0 12  8  4  8 12 12 12  8  4 12 12  0  4  4  8  0  8  8 12  4  0  8  4 12  4  4 12  0  8  8 12 12 12  8
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  8  0  8  0  8  8  0  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+44x^34+178x^35+436x^36+656x^37+1112x^38+964x^39+1537x^40+1024x^41+1006x^42+560x^43+330x^44+168x^45+105x^46+20x^47+32x^48+8x^49+4x^50+6x^51+1x^54

The gray image is a code over GF(2) with n=320, k=13 and d=136.
This code was found by Heurico 1.16 in 0.687 seconds.