The generator matrix

 1  0  1  1  1 X+2  1  1  1  0  1 X+2  1  1  1  0  1  1 X+2  1  1  1  2  1  X  X  1  X  1  1  1  1  1  X  1  0  1  1  X  1
 0  1 X+1 X+2  1  1 X+1  3  0  1 X+2  1  3 X+1  0  1  3 X+2  1 X+1 X+3  2  1  X  1 X+2  3  X X+3  1  1  1 X+3  0 X+3  X  0  2 X+2 X+1
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  0  2  2  0
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  2  0  0  2  0  0  0  2  2  0  2  2  2  0  2  0  2  2  0  0  2  2  2  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  0  2  0  0  2  2  0  0  0  0  2  0  2  0  2  2  0  2  2  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+15x^36+90x^37+33x^38+116x^39+45x^40+92x^41+19x^42+72x^43+2x^44+10x^45+8x^46+4x^47+3x^50+1x^54+1x^68

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 0.0268 seconds.