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  2 2X  X  2
 0 2X+2  0  2  0  0  2 2X+2  0  0  2 2X+2  0  2 2X  0 2X+2 2X  2 2X+2 2X 2X 2X 2X  0 2X+2  2 2X+2  2 2X+2  2 2X  2  2  2 2X+2
 0  0 2X+2  2  0 2X+2  2  0 2X  2 2X+2 2X 2X 2X+2  2  2 2X  2  2  2 2X  2 2X 2X+2 2X 2X+2 2X  2 2X 2X 2X 2X 2X+2  2  0  0
 0  0  0 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0

generates a code of length 36 over Z4[X]/(X^2+2) 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 69.3 seconds.