The generator matrix

 1  0  0  1  1  1 2X+2  0 2X 2X+2  1  1  1  1 X+2  1  1 X+2  1  1 X+2  1  1  1  1  1  1  1  1  1  1 3X+2  1  X  1 3X  1  1
 0  1  0  0  3  3  1 3X+2  1  1 2X 2X+3  2  1 3X 3X 3X+1  1 3X+1 X+2  1 X+1  1  2  2 3X+2  X X+3 2X+2 2X+2  0  1 3X  1 3X+3 3X+2 2X 2X+2
 0  0  1 X+1 3X+3 2X+2 3X+3  1 X+2  1 X+2 2X+1 2X+3 3X  1 2X+3 3X+2 2X+1 X+3  2 X+2  2 X+1 3X+1  1 2X+3  X  1 2X+2 X+3 3X 3X+1 3X+1 3X+2 2X+3  1 X+1 2X
 0  0  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0  0  0 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X  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+176x^34+746x^35+1342x^36+1404x^37+1304x^38+1216x^39+928x^40+632x^41+264x^42+82x^43+71x^44+12x^45+8x^46+4x^47+1x^48+1x^52

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 0.375 seconds.