The generator matrix

 1  0  0  1  1  1 X^2+X X^2+2  1 X^2+2  1 X^2  1  1 X^2+X+2  1 X+2  1  2 X^2+X  1  0  1  1  1  1 X^2 X^2+X  1  1 X^2 X^2+2  1
 0  1  0  0  1 X+3  1  1 X^2+1  1 X^2+X+2  2 X+3 X^2+X+2  1 X+3  X X+2  1  1  1 X+2 X^2 X^2+3  0 X^2  1  1  3 X^2+X+1 X^2 X^2+X+2 X+2
 0  0  1  1  1 X^2+X  1  3  X X^2  1  1 X^2+3 X+2  3 X^2+3  1 X+3 X+2 X^2+X+1 X^2+X+1  1 X^2  0 X^2+1 X^2+X+1 X^2+1 X^2+2 X^2+1 X^2  1  1 X^2+1
 0  0  0  X  2 X+2 X+2 X^2+2 X^2 X^2+X+2 X^2 X^2+X+2 X^2+X+2 X^2+X  0 X^2 X^2+X X^2+2 X+2 X^2+X X^2+X+2  2 X+2  X  2  X  2 X^2+2 X^2+X+2 X^2+X+2 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 28.

Homogenous weight enumerator: w(x)=1x^0+195x^28+1264x^29+1992x^30+4384x^31+4962x^32+7068x^33+5318x^34+4432x^35+1724x^36+1000x^37+232x^38+144x^39+35x^40+12x^41+2x^42+3x^44

The gray image is a code over GF(2) with n=264, k=15 and d=112.
This code was found by Heurico 1.16 in 4.26 seconds.