The generator matrix

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

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+520x^28+2350x^29+4617x^30+7792x^31+10605x^32+13306x^33+11286x^34+8114x^35+4252x^36+1950x^37+549x^38+138x^39+38x^40+10x^41+4x^42+2x^43+2x^47

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 16.5 seconds.