The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X X 1 1 X 2 0 X X 1 2 0 2 X X 2 X 1 X X
0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 2 0 2 0 2 0 2 0 2 2 2 0 0 2 2 0 0 2 0 0 2 2 0
generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+12x^42+1x^44+2x^46
The gray image is a code over GF(2) with n=160, k=4 and d=84.
This code was found by Heurico 1.16 in 0.0176 seconds.