The generator matrix
1 0 1 1 1 X+2 1 1 2 1 1 2 1 X 1 1 X 1 2 1 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X
0 1 1 0 X+3 1 X X+1 1 0 X+1 1 X+2 1 3 0 1 X 1 X+3 X 1 X+3 X+3 3 3 X+3 X 1 3 1 1 X+3 2 2 0 2 X X X+2 X+2 X
0 0 X X+2 X 2 X+2 0 X 2 2 X+2 0 X 0 X X+2 X 2 0 2 0 2 X+2 X+2 2 X 0 X X+2 2 0 X+2 2 X 2 X 0 0 X X 0
0 0 0 2 2 2 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 0 2 0 0 0 2 2 2 2 2 0 2 0 0 2 0 2 2 0 2
generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+296x^40+176x^44+34x^48+4x^56+1x^64
The gray image is a code over GF(2) with n=168, k=9 and d=80.
This code was found by Heurico 1.16 in 2.35 seconds.