The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+126x^50+240x^51+359x^52+496x^53+569x^54+576x^55+551x^56+512x^57+295x^58+208x^59+104x^60+16x^61+30x^62+7x^64+2x^66+1x^68+1x^70+1x^72+1x^90

The gray image is a code over GF(2) with n=440, k=12 and d=200.
This code was found by Heurico 1.16 in 0.344 seconds.