The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+206x^45+1321x^46+3464x^47+6735x^48+9992x^49+15226x^50+18286x^51+20133x^52+18970x^53+15653x^54+9890x^55+6420x^56+2946x^57+1138x^58+452x^59+179x^60+42x^61+4x^62+2x^63+2x^64+2x^65+2x^66+2x^67+2x^68+2x^69

The gray image is a code over GF(2) with n=416, k=17 and d=180.
This code was found by Heurico 1.16 in 99.8 seconds.