The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+124x^34+332x^35+609x^36+652x^37+785x^38+640x^39+508x^40+248x^41+101x^42+36x^43+33x^44+12x^45+12x^46+1x^48+1x^50+1x^54

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 0.141 seconds.