The generator matrix

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

generates a code of length 46 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+222x^43+389x^44+404x^45+237x^46+286x^47+181x^48+192x^49+81x^50+38x^51+4x^53+1x^54+6x^55+4x^56+1x^58+1x^60

The gray image is a code over GF(2) with n=368, k=11 and d=172.
This code was found by Heurico 1.16 in 0.062 seconds.