The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 2X+2  1 X+2  1 3X  1  1  1  1  1  0  1 2X 3X  X 2X+2  2 X+2 3X+2  2  2
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2 3X+3  1  3  1 2X+1  1 2X+2 3X  0 2X X+2  1 3X+2  1  1  1  1  1  1  1 2X+2  2
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0  0 2X  0  0  0 2X  0 2X 2X  0 2X  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+436x^36+168x^38+401x^40+8x^42+8x^44+1x^48+1x^56

The gray image is a code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.16 in 2.72 seconds.