The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+102x^36+718x^37+2219x^38+5168x^39+10466x^40+19186x^41+30025x^42+40746x^43+44250x^44+41186x^45+30465x^46+19628x^47+10331x^48+4736x^49+1879x^50+594x^51+282x^52+116x^53+20x^54+8x^55+6x^56+10x^57+2x^60

The gray image is a code over GF(2) with n=352, k=18 and d=144.
This code was found by Heurico 1.16 in 324 seconds.