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 X 1 1 1 1 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 0
0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 0 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 0
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0 0 2X 2X 0 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+9x^40+30x^41+198x^42+6x^44+9x^46+1x^54+2x^57
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 0.031 seconds.