The generator matrix

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

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+7x^34+34x^35+175x^36+26x^37+9x^38+2x^39+2x^53

The gray image is a code over GF(2) with n=288, k=8 and d=136.
This code was found by Heurico 1.16 in 0.031 seconds.