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

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+120x^49+176x^50+298x^51+355x^52+328x^53+263x^54+212x^55+107x^56+88x^57+40x^58+22x^59+16x^60+16x^61+1x^62+4x^63+1x^84

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 0.172 seconds.