The generator matrix

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

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+358x^33+643x^34+920x^35+733x^36+526x^37+387x^38+288x^39+104x^40+104x^41+16x^42+12x^43+2x^44+2x^46

The gray image is a code over GF(2) with n=288, k=12 and d=132.
This code was found by Heurico 1.16 in 0.093 seconds.