The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  X  X  X
 0  X  0 3X+2  0 X+2  0 3X  2 X+2 2X+2  X  2 3X+2 2X+2 2X 3X 2X X+2 2X  X 2X+2 3X  2 3X+2 3X+2 3X 2X 2X 2X+2 X+2  2  X X+2  X 3X+2 X+2  X
 0  0 2X+2  2 2X 2X+2  2 2X  2  0  0  2 2X+2 2X 2X 2X+2 2X+2 2X 2X  2 2X+2 2X+2  0  0 2X+2  0  2  0 2X+2  2  2 2X 2X  0 2X+2  2 2X+2  2

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+42x^36+132x^37+170x^38+120x^39+36x^40+4x^41+6x^42+1x^64

The gray image is a code over GF(2) with n=304, k=9 and d=144.
This code was found by Heurico 1.16 in 0.047 seconds.