The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+200x^30+1204x^31+3605x^32+8708x^33+16943x^34+31706x^35+42853x^36+51278x^37+43100x^38+32206x^39+17310x^40+8264x^41+3151x^42+1182x^43+289x^44+86x^45+30x^46+22x^47+6x^48

The gray image is a code over GF(2) with n=296, k=18 and d=120.
This code was found by Heurico 1.16 in 277 seconds.