The generator matrix

 1  0  0  1  1  1 3X+2  1  1  1  1  X 2X X+2 3X+2  1  1  1  1 2X+2  0  0  1  1  1  1  0 2X+2  1 X+2 X+2 X+2  1  1  1 3X X+2 2X+2
 0  1  0  0 2X+3 3X+1  1 3X+2 2X+1  1  2  X 3X  1  1 3X+2 3X X+1 3X+1  1  1 3X+2 2X  X X+3 2X+1  1  1 3X  1  1  1  1  2  X  1  1  1
 0  0  1  1  1 2X+2  1 2X+1 3X 3X+1 X+2  1  1 2X+3 3X  X  1  2 X+1  0 3X+3  1 X+1 3X+2  X 2X+2 X+2 2X+1 2X+2  2 X+3 X+1 X+2 3X  2 2X+1  1  X
 0  0  0  X 3X 2X 3X  X 2X+2 X+2  2 X+2 X+2  2 3X+2 3X+2  0 X+2 2X+2 3X  X 2X 3X 2X+2 X+2  X  0 3X+2 3X+2 3X+2 X+2 2X+2 2X X+2 3X 3X+2  0 2X+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+444x^33+1316x^34+2480x^35+3727x^36+5724x^37+5437x^38+5802x^39+3847x^40+2368x^41+968x^42+384x^43+177x^44+72x^45+13x^46+6x^47+2x^50

The gray image is a code over GF(2) with n=304, k=15 and d=132.
This code was found by Heurico 1.16 in 9.31 seconds.