The generator matrix

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

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+395x^40+96x^41+768x^42+448x^43+928x^44+352x^45+580x^46+128x^47+249x^48+120x^50+23x^52+4x^54+3x^56+1x^68

The gray image is a code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 4.44 seconds.