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 X 1
0 2 0 2 0 2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 2 2X+2 0 2X 0 2X 0 2X 2 2X+2 2X+2 2X+2 0 2X 0 2 2 0
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
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
generates a code of length 36 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+8x^34+32x^35+174x^36+30x^37+8x^38+1x^40+2x^53
The gray image is a code over GF(2) with n=288, k=8 and d=136.
This code was found by Heurico 1.16 in 0.031 seconds.