The generator matrix

 1  0  0  1  1  1  2  X  1  1  1 X^2+X  1  X  1  1  0 X^2+X+2  1 X^2+2  1  1  1  1  1  X  0  1  1  1  1  X  1
 0  1  0  X  3 X^2+X+1  1 X^2+X  0 X^2+X+1 X^2+1  1  0  1  X X^2+X  1  1 X+3 X^2+X X^2+X X^2+X+1 X+1 X^2+2 X^2+3  1 X^2  1  3  3 X^2+X+3  1  0
 0  0  1  1  1  X X+1  1 X^2+1 X^2+2 X+1  X  X  1 X^2+X+3 X^2+X+2 X+2 X+3 X^2+X+1  1 X^2 X^2 X^2+X X^2+3  2 X^2+3  1 X^2 X^2+X X^2+X+1 X+3 X^2+3  0
 0  0  0 X^2 X^2+2  2 X^2 X^2+2  2 X^2+2  2 X^2+2 X^2  2 X^2+2  2 X^2+2  2  0  2 X^2  2 X^2+2 X^2 X^2+2 X^2 X^2+2  0 X^2 X^2+2 X^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+95x^28+628x^29+1243x^30+1830x^31+2930x^32+2972x^33+3090x^34+1768x^35+1033x^36+520x^37+167x^38+82x^39+11x^40+8x^41+4x^42+2x^48

The gray image is a code over GF(2) with n=264, k=14 and d=112.
This code was found by Heurico 1.16 in 1.11 seconds.