The generator matrix

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

generates a code of length 33 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+153x^30+376x^31+384x^32+332x^33+325x^34+276x^35+138x^36+20x^37+16x^38+20x^39+5x^40+1x^42+1x^46

The gray image is a code over GF(2) with n=264, k=11 and d=120.
This code was found by Heurico 1.16 in 0.031 seconds.