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

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+9x^34+86x^36+320x^37+86x^38+8x^40+1x^42+1x^72

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.