The generator matrix

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

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+49x^30+390x^31+563x^32+696x^33+818x^34+694x^35+460x^36+274x^37+72x^38+32x^39+16x^40+22x^41+3x^42+4x^43+1x^46+1x^50

The gray image is a code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 0.11 seconds.