The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1  1  1 X^2+X+2  1  1 X^2+2  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1 X^2  2  X  2 X+2  1  1  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3 X+2 X+1  1  2 X^2+X+3  1  X  1  3 X+1 X^2  1 X^2+X X^2+X X^2+3  2 X^2+X+3 X^2+X+2 X^2+1  2 X^2+X+3 X^2+2 X+3 X^2+X X^2+X+2 X^2+3 X^2+1 X^2+2  X  1 X+1  1  1  1  1  1 X^2+X+3 X^2+3 X^2+1
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2+2 X^2+X X^2+X X^2+2 X^2+X+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2  X  0 X^2+2 X^2+X X^2+X X^2+2  2 X+2  0  2  X X+2  0 X^2+X X+2  0  X  2 X^2 X^2  2 X^2 X^2+X+2  0

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+323x^52+340x^53+304x^54+168x^55+285x^56+312x^57+272x^58+8x^59+20x^60+4x^61+8x^64+1x^68+1x^72+1x^80

The gray image is a code over GF(2) with n=440, k=11 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.