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

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+344x^33+768x^34+706x^35+902x^36+392x^37+430x^38+290x^39+160x^40+84x^41+9x^42+8x^43+1x^44+1x^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 0.094 seconds.