The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+150x^46+910x^47+1920x^48+2566x^49+3873x^50+4412x^51+5549x^52+4224x^53+3898x^54+2428x^55+1482x^56+794x^57+338x^58+112x^59+41x^60+32x^61+20x^62+10x^63+7x^64+1x^66

The gray image is a code over GF(2) with n=416, k=15 and d=184.
This code was found by Heurico 1.16 in 8.08 seconds.