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

generates a code of length 38 over Z4[X]/(X^3+2,2X) 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 0.015 seconds.