The generator matrix

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

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+25x^46+156x^47+217x^48+276x^49+512x^50+634x^51+633x^52+584x^53+410x^54+260x^55+177x^56+86x^57+40x^58+26x^59+22x^60+12x^61+5x^62+12x^63+1x^64+2x^65+4x^68+1x^76

The gray image is a code over GF(2) with n=416, k=12 and d=184.
This code was found by Heurico 1.16 in 0.391 seconds.