The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+336x^34+32x^35+740x^36+448x^37+1066x^38+544x^39+564x^40+254x^42+100x^44+6x^46+2x^48+2x^50+1x^64

The gray image is a code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 16 seconds.