The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 2X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  1  X
 0  X  0 3X+2 2X X+2  0  X  2 3X+2 2X+2 3X 2X+2 3X+2 2X+2  X  X  X 2X X+2 3X+2 3X 2X X+2  X 2X+2  0 X+2  2 X+2  2 2X  0 3X  0 3X 3X+2  2
 0  0 2X+2  0 2X 2X+2 2X+2  2  2  2 2X  2  2  0  0 2X 2X 2X+2  0  0  2 2X+2  2 2X 2X  2  0 2X+2 2X+2 2X 2X  2  0 2X 2X 2X+2 2X  2
 0  0  0 2X+2 2X+2  2 2X+2 2X  0  0 2X+2 2X+2  2  0 2X 2X+2 2X 2X 2X+2 2X 2X+2  0  0  0  2 2X+2  2  0 2X+2 2X  2 2X  2 2X  0  2  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+128x^34+72x^35+248x^36+316x^37+564x^38+324x^39+216x^40+44x^41+84x^42+4x^43+28x^44+8x^45+8x^46+2x^48+1x^64

The gray image is a code over GF(2) with n=304, k=11 and d=136.
This code was found by Heurico 1.16 in 0.265 seconds.