The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  2  1  2  2  1  1  1  1  2  1  2  2  2  1  1  2  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  2  2  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  2  2  0  2  0  0  2  0  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  0  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  2  0  0  0  0  2  0  0  0  0  2  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  0  0  0  2  0  0  2  2  0  2  2  2  2  0  0  2  2  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  2  0  0  2  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  2  2  2  0  0  0  2  2  0  2  0  0  2  0  0  0  0  2  2  0  2
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  0  2  0  2  0  2  0  0  0  2  2  2  0  2  0  0  0  0  2  2  2  2  2  0  0

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

Homogenous weight enumerator: w(x)=1x^0+46x^26+119x^28+184x^30+304x^32+513x^34+844x^36+1291x^38+1518x^40+1325x^42+934x^44+531x^46+270x^48+155x^50+84x^52+41x^54+18x^56+9x^58+3x^60+1x^62+1x^64

The gray image is a code over GF(2) with n=80, k=13 and d=26.
This code was found by Heurico 1.16 in 12.2 seconds.