The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+130x^32+112x^34+384x^36+128x^37+540x^38+384x^39+784x^40+384x^41+508x^42+128x^43+372x^44+116x^46+88x^48+4x^50+28x^52+4x^56+1x^64

The gray image is a code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 1.71 seconds.