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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+39x^36+142x^38+183x^40+100x^42+24x^44+14x^46+8x^48+1x^76

The gray image is a code over GF(2) with n=160, k=9 and d=72.
This code was found by Heurico 1.16 in 0.0364 seconds.