The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+398x^35+646x^36+880x^37+709x^38+556x^39+370x^40+264x^41+98x^42+134x^43+30x^44+8x^45+1x^46+1x^48

The gray image is a code over GF(2) with n=304, k=12 and d=140.
This code was found by Heurico 1.16 in 0.109 seconds.