The generator matrix

 1  0  0  1  1  1  2  1  1 X^2+2 X^2+X X^2  1  1  1  1  1  X X+2  0 X^2+X  1  1  X  1  X  1  1  1  1  1 X^2+2  2  1
 0  1  0  2 X^2+1 X^2+3  1 X^2 X^2+2 X^2+X  1  1 X^2+X+1 X+1  3 X^2+X+2  1  1  1  1  1 X+2 X^2+X+3 X^2 X^2+3 X+2  X X^2+X+3 X^2+X  2  0  1  1  2
 0  0  1 X+3 X+1  2 X^2+X+1  X  3  1 X^2+X+2  1 X^2+X+3 X^2+X X+2 X^2+2 X^2+3 X+3  1 X^2+X+2  2 X^2+1  2  1 X^2  1 X^2+X+2  3 X+1 X^2+X+2 X+2 X^2+2 X^2+2  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+316x^31+853x^32+588x^33+842x^34+464x^35+628x^36+208x^37+84x^38+84x^39+22x^40+4x^41+2x^42

The gray image is a code over GF(2) with n=272, k=12 and d=124.
This code was found by Heurico 1.16 in 0.094 seconds.