The generator matrix

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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+36x^53+8x^54+176x^55+14x^56+8x^57+6x^58+1x^64+2x^66+4x^69

The gray image is a code over GF(2) with n=440, k=8 and d=212.
This code was found by Heurico 1.16 in 0.375 seconds.