The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 X X 1 X X 1 X 1 1 1 X X 2X+2 X 2X+2 2X+2 X 2X+2 2X+2 2X+2 2X+2 X 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 2X 2X 0 0
0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 2X 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 0 0 0 2X 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 2X 0 0 0 2X 0 0 2X 2X 0 2X
0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 0 0 2X 0 2X
generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.
Homogenous weight enumerator: w(x)=1x^0+34x^50+16x^51+168x^52+16x^53+8x^54+6x^56+2x^58+1x^64+4x^66
The gray image is a code over GF(2) with n=416, k=8 and d=200.
This code was found by Heurico 1.16 in 0.203 seconds.