The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+374x^33+1401x^34+2420x^35+4056x^36+5184x^37+5896x^38+5440x^39+4125x^40+2096x^41+1138x^42+420x^43+130x^44+56x^45+20x^46+8x^47+2x^49+1x^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 38.2 seconds.