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

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

Homogenous weight enumerator: w(x)=1x^0+8x^34+32x^35+174x^36+30x^37+8x^38+1x^40+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.