The generator matrix

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

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+72x^41+73x^42+140x^43+465x^44+138x^45+62x^46+56x^47+6x^48+10x^49+1x^86

The gray image is a code over GF(2) with n=352, k=10 and d=164.
This code was found by Heurico 1.16 in 0.047 seconds.