The generator matrix

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

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+76x^36+128x^37+104x^38+128x^39+66x^40+8x^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.