The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+126x^33+654x^34+1346x^35+1991x^36+2568x^37+3114x^38+2742x^39+1907x^40+994x^41+558x^42+262x^43+85x^44+20x^45+10x^46+2x^47+4x^49

The gray image is a code over GF(2) with n=304, k=14 and d=132.
This code was found by Heurico 1.16 in 1.47 seconds.