The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+126x^51+204x^52+318x^53+289x^54+290x^55+315x^56+224x^57+90x^58+72x^59+39x^60+40x^61+21x^62+8x^63+10x^65+1x^84

The gray image is a code over GF(2) with n=440, k=11 and d=204.
This code was found by Heurico 1.16 in 0.188 seconds.