The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X X X 2 X 2 X 0 X 0 X 2 X 2 1 1
0 X 0 X+2 0 X+2 0 X 2 X+2 2 X 2 X+2 2 X X+2 X X+2 X 0 2 X X X X X+2 X X+2 X X X X X 0 0
0 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0
0 0 0 2 2 2 2 0 0 0 2 2 2 0 0 2 0 2 2 0 2 2 2 0 0 2 2 0 0 2 0 2 2 0 0 2
generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+16x^34+91x^36+16x^38+2x^40+1x^48+1x^52
The gray image is a code over GF(2) with n=144, k=7 and d=68.
This code was found by Heurico 1.16 in 0.017 seconds.