The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  1  2  X  X  1  2  1  1  1  X  0  1  1  X  1  1  1  X  1  1  1  1  1  1 X+2  1 X+2  1
 0  1  0  0  1  1  1  X  2  3  1  2  3  1  0 X+2  1  1  2  X  1  2  1 X+2 X+3  1  2 X+1 X+2  1  X X+1  1 X+3  X  X  1 X+1  1  0
 0  0  1  1  2  3  1  1  X X+2  X X+1 X+3 X+3  1  1  X  1  3 X+2 X+1  1  2  0  0 X+3  2 X+2 X+3 X+2  3 X+1  2  2  3 X+3 X+3  3  X  0
 0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  0  2  2  2  0  0  2  0  2  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+71x^36+134x^37+154x^38+176x^39+138x^40+92x^41+57x^42+48x^43+47x^44+46x^45+20x^46+16x^47+15x^48+9x^50

The gray image is a code over GF(2) with n=160, k=10 and d=72.
This code was found by Heurico 1.11 in 0.0292 seconds.