The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 X 1 1 X 1 X X 1 1 X X X X X X X 1 1 1 1 1 1 1 1 1 X X 1 1 1 X 1
0 2 0 2 0 2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 2 0 2 0 0 2X 0 2X 2X 2 2X+2 2X+2 0 2X+2 0 2X+2 2X+2 0 2 2X+2 2X 2X 2X 2X 2 2X+2 2 0 2X 2X+2 0 2 2 0
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 0 2X 0 2X 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 2X 0 0 2X 0 0 0 2X
0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 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+8x^50+32x^51+174x^52+30x^53+7x^54+1x^56+2x^69+1x^70
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 0.109 seconds.