The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0  1  1  X  1  1  X  1  1  0  1  X  1  X  1  X  1  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0 X+2  2 X+2  2 X+2  0 X+2  X  0  0 X+2  0  X  2  2 X+2  0  X  X  2 X+2  2  X  X  X X+2 X+2
 0  0  X  X  0 X+2  X  0  2  X  X  0  2 X+2  X  0 X+2  0  2  X  2  0  X X+2  X  X  0  X  2  X X+2  0  0  0  2  X  X X+2 X+2  X
 0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  2  2  2  2  0  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  0  2  2  0  0  0  2  2  2  2  2  0  2  0  0  2  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  0  2  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  0  2  2  0  0
 0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  0  0  2  0  0  0  2  2  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+137x^34+8x^35+180x^36+72x^37+314x^38+176x^39+334x^40+176x^41+274x^42+72x^43+146x^44+8x^45+92x^46+40x^48+13x^50+2x^52+2x^54+1x^64

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 12.5 seconds.