The generator matrix

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

generates a code of length 34 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+212x^31+281x^32+404x^33+394x^34+336x^35+157x^36+168x^37+53x^38+12x^39+8x^40+20x^41+1x^44+1x^46

The gray image is a code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 0.047 seconds.