The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+69x^28+6x^29+103x^30+80x^31+183x^32+170x^33+357x^34+480x^35+1312x^36+1260x^37+3627x^38+6192x^39+5057x^40+6212x^41+3657x^42+1232x^43+1322x^44+494x^45+357x^46+192x^47+187x^48+50x^49+79x^50+16x^51+48x^52+9x^54+11x^56+3x^58+1x^60+1x^64

The gray image is a code over GF(2) with n=320, k=15 and d=112.
This code was found by Heurico 1.16 in 12.9 seconds.