The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  X  X 2X+2  1  X  1  X 2X+2  X  X 2X+2 2X  0  X 2X+2 2X 2X+2 2X+2
 0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X  0

generates a code of length 39 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+27x^40+4x^42

The gray image is a code over GF(2) with n=312, k=5 and d=160.
This code was found by Heurico 1.16 in 0.016 seconds.