The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2+2  1  1  1  X  1  1  1  X  1 X^2  1  2  1  1  X  1  0
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+X+2 X^2+2  X X^2+2 X^2+X X^2+X+2  2 X^2+X+2  2  X X^2+X X^2+X X+2 X^2+X X+2 X^2+X+2 X^2+2 X+2 X+2  X X^2  X X^2+2 X^2+2 X^2+X  0  X
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2  X  X X^2+X+2 X+2  X X+2 X^2+2 X^2+2 X^2+2 X^2+2  0  2 X^2+X+2 X^2+2 X^2+X X+2  X X^2+X  2  X X^2+X  2  2  X X^2+2  0
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0  0 X^2+2  2 X^2 X^2+2  2 X^2  0  2 X^2+2  2  2 X^2  0 X^2 X^2 X^2 X^2  2 X^2+2  2 X^2+2  0 X^2+2 X^2+2  2 X^2

generates a code of length 40 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+400x^36+64x^37+644x^38+448x^39+1100x^40+448x^41+524x^42+64x^43+320x^44+44x^46+34x^48+4x^50+1x^64

The gray image is a code over GF(2) with n=320, k=12 and d=144.
This code was found by Heurico 1.16 in 118 seconds.