The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^51+226x^52+256x^53+280x^54+272x^55+332x^56+256x^57+136x^58+96x^59+46x^60+16x^63+1x^64+2x^72

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 0.125 seconds.