The generator matrix

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

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+637x^28+2144x^29+4494x^30+7972x^31+10872x^32+13084x^33+11334x^34+8016x^35+4249x^36+1952x^37+614x^38+108x^39+47x^40+4x^41+4x^42+2x^44+2x^50

The gray image is a code over GF(2) with n=264, k=16 and d=112.
This code was found by Heurico 1.16 in 15.5 seconds.