The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+44x^37+164x^38+44x^39+1x^42+1x^50+1x^60

The gray image is a code over GF(2) with n=304, k=8 and d=148.
This code was found by Heurico 1.16 in 0.016 seconds.