The generator matrix

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

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+296x^34+144x^35+251x^36+48x^37+202x^38+32x^39+43x^40+4x^42+1x^44+2x^46

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 0.5 seconds.