The generator matrix

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

generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+182x^34+184x^36+118x^38+6x^40+18x^42+2x^46+1x^48

The gray image is a code over GF(2) with n=288, k=9 and d=136.
This code was found by Heurico 1.16 in 70.9 seconds.