The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+338x^35+858x^36+688x^37+780x^38+408x^39+470x^40+260x^41+180x^42+86x^43+14x^44+12x^45+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.