The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  0  1  1  X  1  1  1  1  1 X^2  X X^2+2  1  1  1  X
 0  X  0  X  0  2 X^2+X  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X+2 X^2+X+2 X+2 X^2 X^2+2 X^2+X  0  2  X X^2  X X^2+2 X^2+X X^2+X  0  2 X+2 X^2+X  X  X X^2+2  0 X^2  0 X^2+X X^2+X
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2+2  2  0 X^2+2  X X^2+X X^2+X  X X+2  X  0 X^2+2 X+2  X X^2+2  X  2 X^2+X  0  2 X^2 X^2+X+2  0 X^2+2 X^2+X X^2+X+2 X+2  X X^2  0 X^2+2 X^2+X+2
 0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  2  0  0  0  0  0  2  2  2  2  0  2  2  2  0  0
 0  0  0  0  2  2  0  0  0  2  2  2  0  2  2  2  0  2  0  0  0  0  2  0  0  2  2  0  0  0  2  2  0  0  0  2  2  0  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+403x^36+64x^37+620x^38+448x^39+1148x^40+448x^41+488x^42+64x^43+330x^44+44x^46+34x^48+3x^52+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 102 seconds.