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

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+15x^34+2x^35+126x^36+222x^37+112x^38+30x^39+1x^40+2x^41+1x^66

The gray image is a code over GF(2) with n=296, k=9 and d=136.
This code was found by Heurico 1.16 in 0.032 seconds.