The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X X 1 X^2 X^2 X^2 1 X 1 1 X X X X X^2 1
0 2 0 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 0 2 2 0 0 2 2 0 2 2 0 0 0
0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 0 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+3x^36+50x^37+3x^38+4x^41+1x^42+2x^45
The gray image is a code over GF(2) with n=296, k=6 and d=144.
This code was found by Heurico 1.16 in 0.016 seconds.