The generator matrix

 1  0  1  1  1 X+2  1  1  1 2X+2  1 3X  1  1  1  0  1 X+2  1  1  1  1  0  1 X+2  X  X  1  1  1  1  1  1  X  X  1  0  1
 0  1 X+1 X+2  3  1 3X+3 2X+1 2X+2  1 3X  1  3 X+1  0  1 X+2  1 3X+3 2X+1 3X+3  0  1 X+2  1 3X X+2 3X+3  3 2X+3 2X+3 X+1 2X+1  X  0 3X+1  X 2X
 0  0 2X  0  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X  0 2X
 0  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0  0
 0  0  0  0 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 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+31x^34+272x^35+129x^36+504x^37+196x^38+524x^39+122x^40+200x^41+28x^42+32x^43+2x^44+4x^47+1x^48+1x^50+1x^68

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 0.062 seconds.