The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 X X^2+2 X 2 X X^2 X X X X 1 1 1 1 1 1 1 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2+X X X^2 X X+2 X X^2+X+2 X X X 0 X^2+2 2 X^2 0 2 X^2+2 X^2 X^2+X X^2+X+2 X+2 X
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+120x^36+6x^40+1x^48
The gray image is a code over GF(2) with n=288, k=7 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.