The generator matrix

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

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+100x^28+144x^29+344x^30+412x^31+761x^32+664x^33+668x^34+448x^35+316x^36+120x^37+72x^38+4x^39+18x^40+20x^42+4x^44

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 0.172 seconds.