The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+341x^34+144x^35+436x^36+352x^37+354x^38+144x^39+148x^40+105x^42+22x^44+1x^56

The gray image is a code over GF(2) with n=296, k=11 and d=136.
This code was found by Heurico 1.16 in 82.8 seconds.