The generator matrix

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

generates a code of length 34 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+18x^33+85x^34+18x^35+2x^37+2x^39+1x^42+1x^44

The gray image is a code over GF(2) with n=272, k=7 and d=132.
This code was found by Heurico 1.16 in 0.016 seconds.