The generator matrix

 1  0  1  1  2  1  1  1 X+2  1  1 2X+2  0  1  1  1  1  1 2X+2 2X+2  1  1  1  0 2X 3X  X 3X+2  0  X 3X+2 X+2 3X  1  1  1 2X  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1 3X  0
 0  1  1 X+2  1 X+3  2  3  1 X+1  X  1  1  2 X+1 2X  X  1  1  1 3X+3 3X+2 2X+3  1  1  1  1  1  0  1  1  1  1  0 X+2 3X+3  2  3  X X+2 2X+2 X+1 2X+3  0  1 2X 3X+2 3X+3 X+3 2X+1  1 3X  2  1  1
 0  0  X  0 3X  X 3X 2X  0 2X 3X 3X+2 2X+2 3X+2 2X+2  2 3X+2 X+2 3X+2  X X+2  2 2X+2  0  2 2X  X  X  X 3X+2 X+2 2X+2 2X+2 X+2 3X+2 2X  X X+2  2 3X 2X 3X+2  0  X 3X 2X+2  0  2  X 2X 3X  X X+2  2 3X+2
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X 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+174x^51+488x^52+636x^53+631x^54+588x^55+515x^56+404x^57+279x^58+190x^59+83x^60+28x^61+48x^62+24x^63+4x^65+1x^68+1x^70+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 0.281 seconds.