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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+140x^51+171x^52+348x^53+168x^54+490x^55+168x^56+288x^57+88x^58+104x^59+21x^60+20x^61+16x^62+18x^63+6x^64+1x^88

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 0.188 seconds.