The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1 X^2+2  1  1  1  1 X^2+X+2  1  0  1  1  1  2 X+2  1 X^2+X+2  1  1 X^2  1  1  1  X  1  1  1  0  X  1 X^2  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3 X^2+2  1  X  1 X^2+X+1  3 X+1  0  1 X^2+X+2  1 X+1  2 X+2  1  1 X^2  1 X^2+X+2 X+3  1 X^2+3  1  0  1  X X^2+3 X^2+3  1  2 X+1  1 X^2+2
 0  0 X^2  0  0  0  0  2  2  2  2 X^2  2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2  2  2  0  2  0 X^2 X^2+2  2  2  2 X^2 X^2+2  2  0  2 X^2+2 X^2+2
 0  0  0 X^2+2  2 X^2+2 X^2  2 X^2 X^2  2  2  0 X^2 X^2+2  2  0 X^2 X^2+2  2 X^2  2 X^2 X^2+2  2  0 X^2+2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2+2 X^2 X^2+2 X^2+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+137x^36+428x^37+494x^38+776x^39+454x^40+832x^41+448x^42+376x^43+82x^44+20x^45+30x^46+9x^48+4x^50+5x^52

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 0.157 seconds.