The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  1  2  1  1  1  1  2  2  1  2  2  1  2  1  1
 0  8  0  0  0  0  0  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  0  0  8  8  8  8  0  8
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  8  8  8  0  0  8  8  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  0  0  8  0  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  0  8  0  8  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  8  0  0  8  8  0  8  0  0  0  8  8  0  8  0  8  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  8  8  0  0  0  0  8  0  8
 0  0  0  0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  0  0  8
 0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  0  8  8  0  0  8  0  8  8  0  0  0  0  8  0  8  8  0  8  0  8  8
 0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  0  8  8  0  0  8  8  8  0  0  0  0  0

generates a code of length 40 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+42x^26+122x^28+200x^30+8x^31+245x^32+72x^33+302x^34+288x^35+392x^36+672x^37+466x^38+1008x^39+25092x^40+1008x^41+478x^42+672x^43+420x^44+288x^45+374x^46+72x^47+242x^48+8x^49+130x^50+88x^52+46x^54+20x^56+8x^58+2x^60+2x^62

The gray image is a code over GF(2) with n=320, k=15 and d=104.
This code was found by Heurico 1.16 in 13.3 seconds.