The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+370x^35+710x^36+810x^37+800x^38+490x^39+359x^40+246x^41+167x^42+120x^43+10x^44+8x^45+4x^47+1x^50

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.