The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^40+8x^42+4x^44+1x^48

The gray image is a code over GF(2) with n=80, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00669 seconds.