The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+366x^34+784x^35+712x^36+736x^37+484x^38+536x^39+227x^40+112x^41+118x^42+8x^43+10x^44+2x^48

The gray image is a code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 0.094 seconds.