The generator matrix

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

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+114x^45+1080x^46+2916x^47+6718x^48+11868x^49+20271x^50+30466x^51+36888x^52+40678x^53+37738x^54+31014x^55+20437x^56+11608x^57+6301x^58+2560x^59+944x^60+318x^61+144x^62+34x^63+32x^64+4x^65+2x^66+2x^67+2x^68+2x^69+2x^72

The gray image is a code over GF(2) with n=424, k=18 and d=180.
This code was found by Heurico 1.16 in 436 seconds.