The generator matrix

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

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+44x^41+242x^42+172x^43+188x^44+118x^45+165x^46+32x^47+40x^48+18x^49+1x^50+1x^52+2x^56

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 0.063 seconds.