The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+6x^36+108x^37+6x^38+1x^40+4x^41+1x^42+1x^50

The gray image is a code over GF(2) with n=296, k=7 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.