The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^38+9x^40+2x^42+2x^44

The gray image is a code over GF(2) with n=304, k=6 and d=152.
This code was found by Heurico 1.16 in 0.016 seconds.