The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+76x^40+696x^41+1477x^42+2964x^43+3400x^44+5362x^45+5239x^46+5102x^47+3423x^48+2716x^49+1320x^50+668x^51+137x^52+138x^53+27x^54+16x^55+2x^56+1x^58+1x^60+2x^63

The gray image is a code over GF(2) with n=368, k=15 and d=160.
This code was found by Heurico 1.16 in 6.27 seconds.