The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X 2X+2  X  0  X 2X+2  X  X  X 2X  X  2  X 2X  X  2  1  1
 0  X 2X+2 X+2  0 X+2 2X+2 3X 2X 3X+2  2 3X 2X 3X+2  2  X X+2  X 3X  X X+2  X 3X  X  0 2X+2 3X+2  X  X  X 3X+2  X  X  X  0 2X
 0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X

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+6x^34+36x^35+173x^36+24x^37+10x^38+4x^39+1x^48+1x^52

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.