The generator matrix

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

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+68x^34+116x^35+159x^36+376x^37+146x^38+52x^39+71x^40+32x^41+2x^42+1x^68

The gray image is a code over GF(2) with n=296, k=10 and d=136.
This code was found by Heurico 1.16 in 0.016 seconds.