The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 X X X X X^2 0 X^2 2 1 1 X^2 X X 1 1 X^2 1 1
0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 2 X^2+2 X^2 0 2 X^2+2 X^2 X^2+2 X^2 X^2 X^2 0 2 2 0 2 X^2+2 X^2 0 0 2
generates a code of length 36 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+49x^36+12x^38+1x^40+1x^44
The gray image is a code over GF(2) with n=288, k=6 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.