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 X X X X X X X X X 1 1 1 1 X X
0 2 0 2 0 2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 2 2 0 2X 0 2X 0 2X 2X+2 2X+2 2X+2 2X+2 0 2X 0 2 0 2 0 2X
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 2X
0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 0 2X 2X 0 0
generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+22x^36+212x^38+15x^40+4x^42+2x^56
The gray image is a code over GF(2) with n=304, k=8 and d=144.
This code was found by Heurico 1.16 in 0.031 seconds.