The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X 1 1 X 1 2 2 2 0 0 0 X X X X X 2 1
0 2 0 2 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 0 2 0 2 2 2 2 0 0 0 2 2 0 0 0
0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 0 0
generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+3x^40+22x^41+4x^42+2x^45
The gray image is a code over GF(2) with n=160, k=5 and d=80.
This code was found by Heurico 1.16 in 0.0177 seconds.