The generator matrix

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

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+49x^34+208x^35+325x^36+388x^37+426x^38+468x^39+472x^40+476x^41+444x^42+272x^43+217x^44+152x^45+99x^46+76x^47+9x^48+4x^49+5x^50+4x^53+1x^54

The gray image is a code over GF(2) with n=160, k=12 and d=68.
This code was found by Heurico 1.16 in 0.403 seconds.