The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X X 1 1 1 X X 1 1 1 1 1 1 1
0 2 0 2 0 2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 2 2 0 2X 0 2X 2X+2 0 2X 2X+2 2X+2 2X+2 0 2X 2 0 2X 2 0 0 2 2X+2 0 2X
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 2X
0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 0 2X 0
generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+15x^40+222x^42+15x^44+1x^52+2x^58
The gray image is a code over GF(2) with n=336, k=8 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.