The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X  X  X  X  X  2  0  1  1  2  0  1  1  2 2X  2 2X  1
 0 2X+2  0 2X+2 2X  2 2X  2  0 2X+2  0 2X+2 2X  2 2X+2 2X 2X+2  2  0 2X  2  2  0 2X 2X+2  2  0  0 2X+2  2 2X 2X  2  2  2  2  0
 0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0  0 2X  0 2X 2X  0 2X  0 2X  0  0 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+6x^36+110x^37+6x^38+1x^40+1x^42+2x^45+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 0.031 seconds.