The generator matrix

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

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+188x^34+272x^35+564x^36+624x^37+824x^38+624x^39+546x^40+272x^41+160x^42+7x^44+8x^46+4x^50+1x^52+1x^56

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 0.156 seconds.