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  X  X  X  X  X  X  X  X  1  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  0  2  2  0  2  2  0  2  2  0  0  2
 0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  0  2  2
 0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  2  2
 0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  0  2  0  2  2  0  0  2  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+45x^36+192x^37+15x^40+1x^44+2x^52

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 0.047 seconds.