The generator matrix

 1  0  0  1  1  1  2  0 2X  2  1  1  1  1 3X+2  1  1 X+2  1 3X+2 X+2  1  1  1  1  1  1  1  2 X+2  1  1 3X+2  1  0  1  0  1
 0  1  0  0 2X+3 2X+3  1 X+2  1  1 2X  3 2X+2  1 3X 3X 3X+1  1 X+2  1 2X  3  2 X+3  2 X+1 3X 3X+1  1  1 3X+2 2X+2 X+2 2X+1 3X+2 2X+2  1 3X+2
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1 3X+2 2X+1 2X+3  X  1  3 X+2 X+2  2 3X+1  1 X+1 3X+1  1  1 X+3 3X+2 2X 3X+1  0 2X+3  0  1 2X+1  1 X+2  0  X
 0  0  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  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+262x^34+706x^35+1164x^36+1388x^37+1501x^38+1232x^39+942x^40+508x^41+312x^42+102x^43+28x^44+24x^45+13x^46+8x^47+1x^48

The gray image is a code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 0.36 seconds.