The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+112x^36+664x^37+2181x^38+5392x^39+10309x^40+19490x^41+29756x^42+39686x^43+45673x^44+40892x^45+31169x^46+18898x^47+9689x^48+5190x^49+1940x^50+770x^51+197x^52+80x^53+40x^54+6x^55+3x^56+4x^57+2x^58

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 345 seconds.