The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+1x^38+26x^39+1x^40+2x^41+1x^42

The gray image is a code over GF(2) with n=304, k=5 and d=152.
This code was found by Heurico 1.16 in 0.016 seconds.