The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1  1  X  X  X  1  1  X  1  2  2  2  0  0  0  X  X  X  X  X  2  1
 0  2  0  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  0  2  0  2  2  2  2  0  0  0  2  2  0  0  0
 0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+3x^40+22x^41+4x^42+2x^45

The gray image is a code over GF(2) with n=160, k=5 and d=80.
This code was found by Heurico 1.16 in 0.0177 seconds.