The generator matrix

 1  0  1  1  1  2 X^2+X  1  1  1  1 X^2  1  1 X^2+X+2  1  1  X  1  1 X^2+2  1  1 X+2  1  1  1  X  0  1  X  1  0  1 X^2+2  1
 0  1 X+1 X^2+X+2 X^2+1  1  1 X^2+X X+1  X X^2+X+1  1  2 X^2+3  1 X^2  1  1 X^2+2 X^2+X+3  1 X+2  3  1  2 X^2  2 X^2+X+2  1 X^2+X+3  1  1  X X^2  1 X+3
 0  0 X^2 X^2+2  2 X^2  0  0  2 X^2 X^2+2 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2  0  2  0  0  2  0 X^2+2 X^2  2 X^2+2  2  0  2  0 X^2+2  2 X^2 X^2+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+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 0.516 seconds.