The generator matrix

1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 2 2 2 2 1 1 0 1 0 1 1 1 0 2 1 2 1 1 2 0 0 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3 2 1 1 2 3 1 1 1 1 1 2 3 1 1 3 1 3 1 2 0 1 0 0
0 0 1 0 0 0 0 0 0 1 2 3 3 0 1 2 1 1 0 2 0 1 2 3 1 1 0 1 2 3 2 3 0 0 3 0 1 0 0 0
0 0 0 1 0 0 0 0 1 0 2 1 3 3 2 2 2 3 2 1 2 2 3 0 1 1 0 0 1 3 1 0 0 0 1 1 3 0 0 0
0 0 0 0 1 0 0 0 1 1 3 2 1 2 1 0 1 1 0 3 1 0 3 2 1 1 3 1 3 0 3 2 0 1 1 1 0 0 0 0
0 0 0 0 0 1 0 0 1 2 1 2 3 1 1 3 2 0 1 1 1 0 3 1 1 0 1 3 2 3 2 3 2 2 2 3 1 1 0 0
0 0 0 0 0 0 1 0 1 3 0 3 0 2 3 1 0 2 3 2 1 3 0 0 2 0 3 1 2 3 1 2 1 2 1 3 1 1 0 0
0 0 0 0 0 0 0 1 2 1 3 0 2 1 0 0 3 0 1 1 3 0 2 2 3 1 3 0 0 1 3 1 3 2 1 3 2 1 0 0

generates a code of length 40 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+78x^26+530x^28+1454x^30+2808x^32+4930x^34+7575x^36+9838x^38+10721x^40+10074x^42+8021x^44+4970x^46+2615x^48+1262x^50+449x^52+154x^54+47x^56+8x^58+1x^60

The gray image is a code over GF(2) with n=80, k=16 and d=26.
This code was found by Heurico 1.10 in 109 seconds.