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  X  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  X
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  2  2  2  2  0  2  2  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  2  2  2  2  0  0  0  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  2  2  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  2  2  2  0  2  2  2  0  2  0  0  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  2  2  0  0  0  0  2  0  0  0  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  0  2  2  2  0  2  2  0  0  2  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  0  2  2  0  0  0  0  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  2  0  0  0  2  2  0  0  2  0  0  2  0  2  0  2  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  0  2  2  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 28.

Homogenous weight enumerator: w(x)=1x^0+98x^28+294x^32+530x^36+512x^38+5314x^40+512x^42+558x^44+269x^48+94x^52+9x^56+1x^72

The gray image is a code over GF(2) with n=160, k=13 and d=56.
This code was found by Heurico 1.16 in 3.24 seconds.