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  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  X  1  1  X  1  0
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2 X^2+X+2 X^2  X X^2+2 X+2 X^2 X^2+X+2 X^2+X  2 X^2+2 X^2+X+2 X^2+2 X^2+X X+2 X^2 X^2  X  X X^2 X^2  X X^2+X+2 X^2+2  2 X^2+X  2 X^2 X^2+X+2  0 X^2+X  0  2 X^2+2 X^2+X+2  0 X^2+X+2 X^2+X X+2 X^2+2 X+2 X^2 X^2+X  2  X
 0  0 X^2+2  0  0 X^2+2 X^2 X^2 X^2 X^2+2 X^2 X^2+2  0  2  2  0  0  2 X^2+2  2 X^2 X^2 X^2  0  2 X^2+2 X^2+2  2 X^2  0  2 X^2+2 X^2  0  0  0 X^2  2 X^2 X^2+2  0  0  2 X^2+2 X^2+2  2 X^2+2  0  2 X^2+2 X^2+2  2  0
 0  0  0 X^2+2 X^2 X^2+2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  2 X^2 X^2+2 X^2  2  2 X^2+2  0  2 X^2+2  2 X^2+2 X^2+2  2 X^2+2  2  0 X^2  2 X^2+2  0  2 X^2+2  0 X^2+2  2 X^2 X^2 X^2  2  0 X^2+2  0  0 X^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+164x^49+60x^50+232x^51+336x^52+580x^53+309x^54+160x^55+45x^56+60x^57+14x^58+56x^59+1x^60+28x^61+1x^62+1x^92

The gray image is a code over GF(2) with n=424, k=11 and d=196.
This code was found by Heurico 1.16 in 103 seconds.