The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  X  1  1  1  X  1 X^2 X^2 X^2  X  X
 0 X^2+2  0 X^2  0  0 X^2 X^2  2  2 X^2 X^2+2 X^2+2 X^2+2  0  2  2 X^2  2 X^2 X^2 X^2 X^2+2 X^2  2  0  0 X^2+2 X^2+2  0 X^2+2 X^2+2  2
 0  0 X^2+2 X^2  0 X^2+2 X^2+2  0  2 X^2 X^2  0  2 X^2  2 X^2 X^2+2 X^2 X^2  0 X^2+2 X^2  2  0  0  2 X^2+2 X^2+2  0 X^2+2  0 X^2+2 X^2
 0  0  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2  2  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0  0  2  0  0
 0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  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+79x^28+16x^29+182x^30+128x^31+406x^32+480x^33+382x^34+128x^35+139x^36+16x^37+42x^38+43x^40+2x^42+2x^44+2x^48

The gray image is a code over GF(2) with n=264, k=11 and d=112.
This code was found by Heurico 1.16 in 0.078 seconds.