The generator matrix

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

generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+254x^34+336x^35+664x^36+612x^37+924x^38+800x^39+1020x^40+916x^41+870x^42+672x^43+586x^44+188x^45+202x^46+48x^47+59x^48+12x^49+20x^50+6x^52+2x^54

The gray image is a code over GF(2) with n=160, k=13 and d=68.
This code was found by Heurico 1.16 in 55.9 seconds.