The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+258x^40+1362x^41+3336x^42+5280x^43+7500x^44+9756x^45+10540x^46+9892x^47+7873x^48+5112x^49+2778x^50+1224x^51+414x^52+116x^53+48x^54+20x^55+16x^56+6x^57+2x^58+2x^60

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 22.4 seconds.