The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+103x^44+116x^45+131x^46+56x^47+55x^48+20x^49+27x^50+1x^52+1x^54+1x^66

The gray image is a code over GF(2) with n=368, k=9 and d=176.
This code was found by Heurico 1.16 in 0.078 seconds.