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

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+412x^35+654x^36+800x^37+777x^38+548x^39+342x^40+312x^41+110x^42+92x^43+34x^44+8x^45+1x^46+4x^47+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.