The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  X  1  1  X
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2 X^2 X+2  0  2 X^2+X X^2+X+2 X^2+2 X+2  2  0 X+2  X  0 X^2+X X+2  0 X^2+X X^2+X+2  2 X^2+2 X^2+X+2 X^2+X
 0  0  2  0  0  0  0  2  0  2  0  2  2  0  0  0  2  2  2  0  2  2  0  2  2  2  2  2  0  2  0  0  2  0
 0  0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  2  2  2  0  0  2  0  0  0  2  0  2  0  2  2
 0  0  0  0  2  0  0  2  2  2  0  0  0  2  0  2  2  2  2  2  2  2  2  0  2  0  0  0  0  0  0  2  0  2
 0  0  0  0  0  2  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  2  0  0  0  0  2  0  0  2  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+159x^30+265x^32+1228x^34+234x^36+140x^38+10x^40+8x^42+1x^44+1x^46+1x^60

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 145 seconds.