The generator matrix

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

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+124x^35+475x^36+284x^37+416x^38+260x^39+303x^40+68x^41+72x^42+24x^43+10x^44+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.