The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+164x^31+1189x^32+3872x^33+9022x^34+18500x^35+30059x^36+43500x^37+48025x^38+45068x^39+31280x^40+18178x^41+8082x^42+3524x^43+1235x^44+280x^45+117x^46+24x^47+12x^48+10x^49+2x^50

The gray image is a code over GF(2) with n=304, k=18 and d=124.
This code was found by Heurico 1.16 in 297 seconds.