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

generates a code of length 44 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+198x^40+96x^41+132x^42+352x^43+504x^44+288x^45+248x^46+32x^47+184x^48+4x^50+8x^52+1x^80

The gray image is a code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.125 seconds.