The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^45+1491x^46+3512x^47+6190x^48+10322x^49+14858x^50+18784x^51+19755x^52+19570x^53+15508x^54+10266x^55+5697x^56+2880x^57+1296x^58+452x^59+197x^60+62x^61+29x^62+10x^63+2x^65+2x^66

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 112 seconds.