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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+34x^29+91x^30+162x^31+236x^32+286x^33+416x^34+994x^35+1560x^36+2588x^37+3602x^38+2668x^39+1580x^40+948x^41+410x^42+380x^43+166x^44+98x^45+81x^46+18x^47+39x^48+14x^49+6x^50+2x^51+2x^52+2x^54

The gray image is a code over GF(2) with n=304, k=14 and d=116.
This code was found by Heurico 1.16 in 3.59 seconds.