The generator matrix

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

generates a code of length 33 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+238x^27+1424x^28+4004x^29+8662x^30+15194x^31+22603x^32+25928x^33+23720x^34+15836x^35+8192x^36+3438x^37+1360x^38+346x^39+68x^40+36x^41+16x^42+2x^43+2x^45+2x^46

The gray image is a code over GF(2) with n=264, k=17 and d=108.
This code was found by Heurico 1.16 in 62.1 seconds.