The generator matrix

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

generates a code of length 34 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+130x^27+947x^28+2722x^29+8158x^30+16394x^31+31378x^32+44432x^33+53180x^34+44634x^35+32521x^36+16544x^37+7480x^38+2310x^39+905x^40+296x^41+76x^42+20x^43+8x^44+6x^45+2x^46

The gray image is a code over GF(2) with n=272, k=18 and d=108.
This code was found by Heurico 1.16 in 246 seconds.