The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+484x^41+762x^42+634x^43+701x^44+542x^45+430x^46+230x^47+113x^48+134x^49+38x^50+16x^51+1x^52+8x^53+2x^54

The gray image is a code over GF(2) with n=352, k=12 and d=164.
This code was found by Heurico 1.16 in 0.125 seconds.