The generator matrix

 1  0  1  1  1 X^2+X  1  1  1 X^2+2  1 X+2  1  1  1  0  1  1 X^2+X  1  1  1  1  1  1  1 X^2+2 X^2+X X^2+2  1  1  X  0  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3  3 X^2+2  1 X+2  1 X^2+1 X+1  0  1 X^2+X+3 X^2+X  1 X^2+1 X^2+X+3  3  0 X+2 X+2 X+1  1  1  1  3 X+1 X^2+2  X  0
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0  2  0  0
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  0  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  2  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+78x^30+142x^31+224x^32+468x^33+246x^34+464x^35+187x^36+140x^37+91x^38+2x^39+1x^40+2x^44+1x^46+1x^52

The gray image is a code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 0.047 seconds.