The generator matrix

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

generates a code of length 33 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+140x^29+214x^30+648x^31+598x^32+1018x^33+492x^34+614x^35+196x^36+120x^37+30x^38+12x^39+4x^40+2x^41+6x^43+1x^48

The gray image is a code over GF(2) with n=264, k=12 and d=116.
This code was found by Heurico 1.16 in 67.2 seconds.