The generator matrix

 1  0  0  0  1  1  1  2  1  1 X^2+X+2 X^2+X+2 X^2+X  1  1  1  1  1 X^2+X+2  0  1  1 X+2  X  0  1 X^2 X^2+X+2  1  1 X^2+2  1  1  1  X  2  1  1 X^2+2  1 X^2 X^2+2  1  1 X^2  1
 0  1  0  0  2  1  3  1 X^2+X+2 X^2+X X^2+X+2  1  1 X^2+3 X^2+1 X+2  0 X+3 X^2  1 X^2+X X^2  0  1  1 X^2+X+1 X^2+X  1  2 X^2  1 X^2+X+1 X^2+X+1 X^2+X+3  1  2 X^2+1 X+1  1 X^2  1  X  1 X^2+X+3  1  2
 0  0  1  0  3  1  2  3  0  1  1 X^2+1 X^2+2 X+2 X^2+X+1  X X^2+X+2 X^2+X+3 X+2 X^2+3 X+3 X^2+3  1 X+1 X+2 X^2+2  1 X^2+3 X+2 X+3 X+1 X^2+3 X^2+X+2  2 X^2+X  X X+1  0 X^2+X+3 X^2+X+3 X+2 X^2+2  3 X^2 X^2+X+1  2
 0  0  0  1  1  2  3  3 X^2+X+1  X  3 X^2+X+2 X+3 X^2+X+2 X^2+3 X^2+1 X^2+2 X+1  1 X^2+X+1 X+2 X+3 X^2+1  2 X^2+2 X^2+2 X^2 X^2+2 X^2+X+1 X^2+X X+2 X^2+1 X+3 X^2+X X+1  1  X X^2+X+1 X+3 X^2  3  1  X X^2+3 X+2 X^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+204x^40+1578x^41+3107x^42+5298x^43+7511x^44+10000x^45+10037x^46+10246x^47+7922x^48+5118x^49+2517x^50+1368x^51+385x^52+164x^53+51x^54+14x^55+9x^56+4x^57+2x^59

The gray image is a code over GF(2) with n=368, k=16 and d=160.
This code was found by Heurico 1.16 in 23.3 seconds.