The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^40+4x^44+1x^48+1x^56

The gray image is a code over GF(2) with n=320, k=7 and d=160.
This code was found by Heurico 1.16 in 0.031 seconds.