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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+143x^50+228x^51+347x^52+406x^53+674x^54+684x^55+565x^56+418x^57+264x^58+128x^59+122x^60+38x^61+32x^62+16x^63+20x^64+2x^65+6x^66+1x^68+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 0.375 seconds.