The generator matrix

 1  0  0  1  1  1  X X+2  0  2  1  1 X+2  1  1  1  1  1  0  1  X  X  1  1  X  1  0  X  1  X  1  1  1  2  1  X X+2  1  1  1
 0  1  0  X  1 X+3  1  1  1  X  2  X  0  3  1  1 X+3 X+2  1 X+2  1 X+2 X+2 X+1  1 X+2  1  X X+3  1  3  0  2  1  3  1  2  3 X+2  0
 0  0  1  1 X+3 X+2  1 X+1 X+2  1  X X+3  1  3  X  2  1  X  1 X+1  3  1  2 X+1  0  X X+3  1  2  2  3 X+1 X+3  2 X+2  X  1  1  2  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  0  2  0  2  0  2  0  0  2  0  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  0  2  0  2  0  2  0  2  2  2  0  2  0  2  2  2  0  2
 0  0  0  0  0  2  0  2  2  2  0  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  0  0  2  2  2  2  2  0  0  2  0  0  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+59x^34+158x^35+333x^36+380x^37+577x^38+422x^39+453x^40+334x^41+485x^42+308x^43+279x^44+136x^45+87x^46+38x^47+18x^48+14x^49+8x^50+2x^51+4x^52

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 0.396 seconds.