The generator matrix

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

generates a code of length 34 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+173x^30+670x^31+1243x^32+1350x^33+1577x^34+1272x^35+1046x^36+516x^37+193x^38+66x^39+46x^40+30x^41+9x^42

The gray image is a code over GF(2) with n=272, k=13 and d=120.
This code was found by Heurico 1.16 in 0.281 seconds.