The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2 X^2+X+2  1  X  1  1  1  X  1  1 X^2  2  X X+2  2  1  2  1  1  1  1  1  1  1  0  1 X^2+X+2  1  1  1  1  1 X^2+X+2  2  X  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+3  1 X^2+X+1 X^2+2  X  1  X X+1  1  1  1  1  1 X^2+X  1 X^2+X+3 X^2+X  1 X^2+2 X^2+X+1  2  X  1 X^2+X+3  1 X^2+X+2 X+1 X^2+X+2  0 X^2+2  1  1 X^2+2 X+2
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+2  X  X X^2+2  0 X^2+X+2  0 X^2+2 X^2+X+2  X X^2+2 X^2+X+2 X^2+X+2  2 X^2+X+2 X^2+2  2  2 X^2 X^2+X X+2  X X+2 X^2+X+2 X^2+2  X X^2+2 X^2+X+2 X^2+2 X^2+X+2 X^2 X^2+2  X X^2+X  0
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  0  0  2  2  2  2  0  2  2  2  0  2  0  0  0  0  0  2  0  2  0  0  0  2  0  2  2  2  0  2

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+208x^49+502x^50+536x^51+648x^52+496x^53+572x^54+460x^55+365x^56+180x^57+60x^58+28x^59+17x^60+12x^61+8x^62+2x^66+1x^76

The gray image is a code over GF(2) with n=424, k=12 and d=196.
This code was found by Heurico 1.16 in 0.265 seconds.