The generator matrix

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

generates a code of length 52 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+139x^44+1016x^45+2926x^46+6122x^47+12117x^48+20240x^49+29319x^50+38390x^51+41257x^52+37830x^53+30963x^54+20464x^55+11568x^56+5876x^57+2399x^58+1008x^59+318x^60+110x^61+52x^62+14x^63+8x^64+4x^66+2x^67+1x^70

The gray image is a code over GF(2) with n=416, k=18 and d=176.
This code was found by Heurico 1.16 in 450 seconds.