The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  2 2X+2  0  1  1 X+2 X+2  1  1 3X 3X+2 3X  1  1 2X+2  1  1  1 3X  1 3X+2  1  1  1  2  1  1  1 2X+2  1  X  1  1  2  2  X  1  1  0 3X 3X+2  1 2X+2  1
 0  1  0 2X  3 2X+3  1  X X+3 3X 3X+3  1  X  1 3X+1  0  1  X  2 2X+1  1  1  1 X+2  X  1 X+3 3X+1  2  2  1  1 2X+1 X+1 3X+2  1 X+2 3X  3  1 3X+3 3X 2X+1 2X+2  1  1  1  2 2X+3  1  1 3X+2 3X+1 3X+2 2X
 0  0  1 3X+1 X+1 2X X+1  X 2X+1  1 3X 3X  1  3  2 3X+2 X+2  1  3 2X+1 2X+3 2X+2 X+3 3X+3  0 X+1 X+1 X+2 2X  1 3X+3  0 3X+2 X+3 2X+2 2X+1  X 3X+1  3  2  3  1 3X  2 2X 3X+2 X+2 3X+3  1 2X+2  0  1  3  1 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+64x^51+574x^52+566x^53+884x^54+498x^55+521x^56+266x^57+381x^58+96x^59+103x^60+76x^61+53x^62+2x^63+9x^64+1x^66+1x^74

The gray image is a code over GF(2) with n=440, k=12 and d=204.
This code was found by Heurico 1.16 in 0.157 seconds.