The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1x^36+26x^37+2x^38+2x^39

The gray image is a code over GF(2) with n=288, k=5 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.