The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 2X+2  1 X+2  1 X+2  1  1  1  1  1  1  1  1  1  1 2X+2  2 3X+2 3X
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2 3X+3  1  3  1  3  1  0 X+2 2X+2 2X+3 2X+1 X+1 3X+1 2X 3X+2 3X  1  1  1  1
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X  0 2X 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+354x^34+316x^36+348x^38+2x^42+3x^48

The gray image is a code over GF(2) with n=288, k=10 and d=136.
This code was found by Heurico 1.16 in 50.1 seconds.