The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  X  1  X  1  1  1  1  X  1  0  1  0  1  0  X  X  1
 0  X  0  0  0  X X+2  X  2  2  X  0  0  X  X X+2  0  0 X+2  X  X  2  X X+2  X  2 X+2  2  X  X  0 X+2  X  2  0  2  X  X  X  0
 0  0  X  0  X  X  X  0  2  0 X+2  X X+2  0 X+2  0  2 X+2  2 X+2  2  0 X+2  X  X X+2  X  X X+2 X+2 X+2  0  X X+2  X  0  2  0  2  0
 0  0  0  X  X  0  X X+2  0  X  2  X  2 X+2  X  0  2  X  X  0 X+2 X+2  0 X+2  2 X+2  2  2 X+2  X  0 X+2 X+2  2  0  X  2  2  X  0
 0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  2  2  0  0  0  2  2  2  0  2  0  2  2  2  2  0  2  2  0  2  2  0  2  0  0
 0  0  0  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  0  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  2  0  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+108x^34+16x^35+239x^36+80x^37+307x^38+160x^39+325x^40+160x^41+247x^42+80x^43+150x^44+16x^45+89x^46+46x^48+17x^50+6x^52+1x^60

The gray image is a code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.192 seconds.