The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+294x^44+171x^48+42x^52+4x^56

The gray image is a code over GF(2) with n=184, k=9 and d=88.
This code was found by Heurico 1.16 in 3.23 seconds.