The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X X^2+2 1 1 X 2 1 1 X X^2 1 1 1 1 X X X X X 0 X X^2+2 1 1 X X 2 X^2 1 1 X^2 0 X^2 2 X X 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X X^2+X X X+2 X 0 X^2+X X^2+X+2 X X^2+2 X+2 X X 2 X^2 X^2+X+2 X 0 X^2+2 2 X^2 X^2+X X X+2 X 0 X^2+2 X^2+X+2 X X X 2 X^2 X^2+2 X^2 X^2 X^2 0 2 0
generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+4x^54+104x^55+7x^56+4x^57+3x^58+4x^61+1x^66
The gray image is a code over GF(2) with n=440, k=7 and d=216.
This code was found by Heurico 1.16 in 0.079 seconds.