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 1 X X X X X X 1 1 1 X X 1 1 1 1 1 1 2X+2 X
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 0 2X+2 0 2X 2X+2 2X+2 2X+2 2X 2 2X+2 0 2X 0 2 0 2 0 2 2X 2
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 0
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 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 0 0 2X
generates a code of length 44 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+28x^42+16x^43+167x^44+16x^45+20x^46+5x^48+1x^52+2x^60
The gray image is a code over GF(2) with n=352, k=8 and d=168.
This code was found by Heurico 1.16 in 0.062 seconds.