The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+78x^31+120x^32+170x^33+200x^34+426x^35+648x^36+1396x^37+2198x^38+1364x^39+604x^40+416x^41+206x^42+164x^43+88x^44+60x^45+18x^46+14x^47+10x^48+6x^49+2x^50+2x^51+1x^64

The gray image is a code over GF(2) with n=304, k=13 and d=124.
This code was found by Heurico 1.16 in 48.4 seconds.