The generator matrix

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

generates a code of length 37 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+18x^36+96x^37+6x^38+4x^40+2x^46+1x^56

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 0.015 seconds.