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

generates a code of length 44 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+184x^41+441x^42+326x^43+354x^44+200x^45+270x^46+148x^47+74x^48+24x^49+9x^50+6x^51+8x^53+3x^56

The gray image is a code over GF(2) with n=352, k=11 and d=164.
This code was found by Heurico 1.16 in 0.063 seconds.