The generator matrix

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

generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+172x^33+448x^34+302x^35+387x^36+220x^37+252x^38+138x^39+76x^40+20x^41+19x^42+12x^43+1x^46

The gray image is a code over GF(2) with n=288, k=11 and d=132.
This code was found by Heurico 1.16 in 0.032 seconds.