The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 X X X X X^2 0 1 1 X^2 2 X X X^2 1 1 X^2 2 2 1
0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 X^2+2 2 X^2 0 2 X^2+2 X^2 X^2+2 X^2 0 2 X^2 X^2 0 2 2 X^2+2 X^2 0 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+3x^36+40x^37+3x^38+16x^39+1x^42
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 0.015 seconds.