The generator matrix

 1  0  1  1  1  2  1  1  0  0  1  1  1  0  1  1  1  2  2  1  1  X  1  1  X  1  1  1  0  1  1  1 X+2  1  1  1  2 X+2  1 X+2
 0  1  1  0  1  1  2 X+1  1  1  2 X+3  0  1  1 X+1  2  1  1  2  3  1  X  1  1  X X+3  2  1  X  3 X+3  1 X+1 X+2 X+1  1  1 X+3  1
 0  0  X  0  0  0  0  2 X+2  X X+2 X+2  0  X X+2  2  X  0  2 X+2 X+2 X+2  X  2  X  X  0 X+2  0  0  X  2  2  X  2  2  0  0  0 X+2
 0  0  0  X  0  0  2  2  2  2  0  2 X+2 X+2 X+2 X+2  X  X X+2  X X+2  X  X  X X+2  2  0  0  0  X  0  X  0 X+2  0  X  2  X  X  2
 0  0  0  0  X X+2 X+2  2  X  0  0 X+2 X+2  2 X+2  X X+2  2  X  0  0 X+2 X+2  X X+2  X X+2 X+2  2  2  2  2  2  0  2  X  2  2  0  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+118x^34+92x^35+420x^36+172x^37+672x^38+248x^39+748x^40+248x^41+618x^42+172x^43+347x^44+92x^45+68x^46+42x^48+28x^50+9x^52+1x^56

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 0.476 seconds.