The generator matrix

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

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+19x^36+104x^37+28x^38+336x^39+35x^40+400x^41+27x^42+16x^43+9x^44+40x^45+8x^46+1x^74

The gray image is a code over GF(2) with n=320, k=10 and d=144.
This code was found by Heurico 1.16 in 0.063 seconds.