The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+137x^28+468x^29+1246x^30+2082x^31+2832x^32+3192x^33+2628x^34+1926x^35+1091x^36+492x^37+216x^38+22x^39+35x^40+8x^41+4x^42+2x^43+2x^46

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 1.14 seconds.