The generator matrix

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

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+78x^36+352x^38+78x^40+2x^44+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.