The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+9x^54+54x^55+141x^56+32x^57+6x^58+8x^59+2x^60+2x^71+1x^78

The gray image is a code over GF(2) with n=448, k=8 and d=216.
This code was found by Heurico 1.16 in 0.125 seconds.