The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+130x^45+1092x^46+3138x^47+6561x^48+11824x^49+20053x^50+29570x^51+37465x^52+41540x^53+38383x^54+30212x^55+20368x^56+11546x^57+5906x^58+2676x^59+1061x^60+374x^61+163x^62+50x^63+16x^64+10x^65+3x^66+2x^67

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 425 seconds.