The generator matrix

 1  0  1  1  1 X+2  1  0  1  1 X+2  1  1  2  1  1  1  0  1  1  X  1  1  1  X  1  1  1  2  1  1  2  X  1  1  1  1  1  0  1
 0  1  1  0 X+3  1  X  1 X+3  1  1  2  X  1  X X+1 X+1  1  3 X+2  1  1  0  1  1 X+2  1  3  1  1  0  1  1  0  2 X+2  X  3  X  2
 0  0  X  0 X+2  0  0  X  2  2 X+2  X X+2  X  X  X  0  0  X  2 X+2  0  X  2  2 X+2  0  2 X+2  2  X  0  0  0  2 X+2  0  X X+2  0
 0  0  0  X  0  0 X+2  X X+2 X+2  X  2  0  2  X X+2  0  X X+2  0  2  2  X X+2  X X+2  X  2  0  2 X+2  2  0  0  0  0  X  X  X  X
 0  0  0  0  2  0  2  2  0  2  0  2  0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  0  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  2  2  0  0  0  0  0  2  0  2  2  2  0  2  0  0  0  2  2  0  2  2  2  0  2  2  2  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+125x^34+88x^35+386x^36+328x^37+525x^38+368x^39+572x^40+336x^41+504x^42+312x^43+255x^44+104x^45+134x^46+26x^48+23x^50+7x^52+1x^54+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 0.503 seconds.