The generator matrix

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

generates a code of length 33 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+40x^28+194x^29+189x^30+616x^31+543x^32+1022x^33+555x^34+536x^35+144x^36+118x^37+54x^38+64x^39+8x^40+10x^41+1x^42+1x^54

The gray image is a code over GF(2) with n=264, k=12 and d=112.
This code was found by Heurico 1.16 in 0.141 seconds.