The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^36+136x^37+94x^38+176x^39+33x^40+8x^41+1x^50+1x^58

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 0.031 seconds.