The generator matrix

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

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+494x^41+648x^42+792x^43+740x^44+488x^45+296x^46+304x^47+147x^48+134x^49+21x^50+24x^51+4x^53+2x^54+1x^58

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 0.141 seconds.