The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+129x^50+16x^51+97x^52+224x^53+329x^54+544x^55+253x^56+224x^57+123x^58+16x^59+27x^60+43x^62+5x^64+16x^66+1x^96

The gray image is a code over GF(2) with n=440, k=11 and d=200.
This code was found by Heurico 1.16 in 41.4 seconds.