The generator matrix

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

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+498x^51+868x^52+1166x^53+1377x^54+1160x^55+961x^56+844x^57+432x^58+378x^59+271x^60+158x^61+53x^62+12x^63+2x^64+8x^65+2x^66+1x^68

The gray image is a code over GF(2) with n=440, k=13 and d=204.
This code was found by Heurico 1.16 in 0.687 seconds.