The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  2  1  0  1  1  1 X+2 X+2  1  1  1  0  1  1 X+2  2 X+2  1  1  1  X X+2  1  1  1  1  1  0
 0  1  0  0  1  1  1  2  0  0  1  1  1  1  1  X X+1  2  1  X  1 X+1  0  1 X+2 X+3  1  1  X X+3 X+3 X+1  1  1  3  0  X X+2  2  1
 0  0  1  1  2  3  1  1  0  1  2  2  3  3  1 X+3  0  X X+2  1 X+3  2  X  X  1 X+3 X+1 X+1  1  3 X+3 X+3  X  0 X+1 X+3  2 X+3  X X+1
 0  0  0  X  0  X  X  X X+2  2  X X+2  0  2 X+2  X  2  0  2  X  2  X X+2  X X+2 X+2  X  2 X+2  X  0  2 X+2  0  0  0  0  X  X  X

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+356x^36+516x^38+484x^40+296x^42+274x^44+84x^46+35x^48+2x^52

The gray image is a code over GF(2) with n=160, k=11 and d=72.
This code was found by Heurico 1.11 in 0.544 seconds.