The generator matrix

 1  0  0  0  1  1  1  1  2  1  1 X+2  0  1  0  0  1  1  1  X  1  1  X  1  1  1  1  1  2 X+2  1  1  2  X  1  X  0  0  1  X
 0  1  0  0  0  1  2  3  1  2 X+3  1 X+2  3  1  X  3 X+1  0  1  X  0  X  1 X+3 X+2  2  3  1  1  3 X+1  1  2 X+2 X+2  1  1  1  0
 0  0  1  0  0  1  3  2  3 X+1  1 X+3  1  X X+2  1 X+2  0  3  1 X+1 X+2  1  3  3 X+2  X X+3  0 X+2  2 X+3  X  1  3  1 X+1  X  X  1
 0  0  0  1 X+1  2 X+3 X+1 X+1  X X+1  2  3  0  1 X+2 X+1  2  1  1  X  1 X+1 X+3 X+2 X+3  X  2 X+3  3  3 X+1  X  2 X+1 X+2 X+1  X  0  1
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  2  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+191x^34+352x^35+677x^36+684x^37+1002x^38+760x^39+1023x^40+816x^41+876x^42+640x^43+543x^44+252x^45+214x^46+72x^47+60x^48+8x^49+21x^50

The gray image is a code over GF(2) with n=160, k=13 and d=68.
This code was found by Heurico 1.13 in 0.642 seconds.