The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+200x^35+407x^36+404x^37+474x^38+408x^39+504x^40+376x^41+400x^42+288x^43+289x^44+182x^45+86x^46+48x^47+5x^48+12x^49+8x^50+2x^52+2x^53

The gray image is a code over GF(2) with n=160, k=12 and d=70.
This code was found by Heurico 1.16 in 0.362 seconds.