The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+33x^28+4x^29+60x^30+36x^31+137x^32+100x^33+160x^34+294x^35+345x^36+666x^37+2817x^38+944x^39+5170x^40+944x^41+2852x^42+676x^43+347x^44+304x^45+163x^46+92x^47+82x^48+28x^49+72x^50+6x^51+27x^52+2x^53+15x^54+2x^56+4x^58+1x^62

The gray image is a code over GF(2) with n=320, k=14 and d=112.
This code was found by Heurico 1.16 in 3.52 seconds.