The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  1  X  1  1  2  X  1  X  X  1  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2 X+2  2  0  X X^2+X+2  X X^2+X X^2 X^2+X+2  0  X X^2+2  2 X^2 X^2+X  0  X X^2+X  2  X X+2  0  X
 0  0 X^2+2  0 X^2 X^2  2 X^2  0  2  0  0 X^2 X^2+2 X^2 X^2  2 X^2+2 X^2 X^2  2 X^2 X^2+2  0 X^2+2 X^2+2 X^2 X^2+2  2  2 X^2  0 X^2 X^2+2
 0  0  0  2  0  0  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  2  0  0
 0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  0  2  0  2  0  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+93x^30+128x^31+261x^32+320x^33+498x^34+336x^35+192x^36+96x^37+73x^38+16x^39+20x^40+8x^42+5x^44+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 0.078 seconds.