The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2 X^2+X+2  1  1 X^2  1  1  X  1  1  1 X^2+X+2  1  1  1  X  1  0  1  1  X  2  1  1 X+2  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3  1 X^2+1  2  1  X X+1 X^2+X  1 X+3 X^2+X+1  0  1 X^2+X+1  1 X^2 X^2+X X^2+X  1  1  X  1 X^2+2
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2 X^2+2 X^2+X+2 X^2+2 X+2 X^2+X+2 X^2+2 X^2+X+2 X^2+2 X^2+X+2 X^2+X  X X^2 X^2+X X^2+X  0 X^2+2 X^2+X  0  2 X^2+X X+2 X^2+X X^2+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+166x^35+408x^36+308x^37+405x^38+234x^39+328x^40+124x^41+35x^42+20x^43+4x^44+4x^45+8x^47+2x^48+1x^52

The gray image is a code over GF(2) with n=304, k=11 and d=140.
This code was found by Heurico 1.16 in 0.047 seconds.