The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^36+6x^40+1x^48

The gray image is a code over GF(2) with n=288, k=7 and d=144.
This code was found by Heurico 1.16 in 0.015 seconds.