The generator matrix
1 1 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 X X 2X+2 2X+2 X 2X+2 X 2X+2 2X+2 1 1 1 1 2X+2 2X+2 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 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 0 2X 2X 2X 0 2X 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 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 0 2X 2X 2X 0 0 2X 0 2X 0 0 2X 0 0 2X 0
0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 0 2X 0 2X 0 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 0 0 2X 2X 2X 0 2X 0 0
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 0 2X 2X 2X 2X 0 0 2X 2X 0 0 0 2X 0 2X 2X 0 0 2X 2X 2X 2X 0 2X 0 0 0 0 2X 0
generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 53.
Homogenous weight enumerator: w(x)=1x^0+36x^53+8x^54+176x^55+14x^56+8x^57+6x^58+1x^64+2x^66+4x^69
The gray image is a code over GF(2) with n=440, k=8 and d=212.
This code was found by Heurico 1.16 in 0.375 seconds.