The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1 2X  1  1 3X+2  1  1  1  1  2  X  X  X  0  X  X 2X+2  1  1 2X+2  X  X  X  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1 2X 3X+1  1 3X+2 2X+3  1  2 X+3  X  1  1  1  0 X+2  X 2X+2 3X  X 2X+2 3X+3  1  2  X 2X  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+79x^36+108x^37+38x^38+22x^39+2x^40+4x^41+2x^43

The gray image is a code over GF(2) with n=296, k=8 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.