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 2 2 2 0 0 0 X 1 1 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 2 2 2 2 0 0 0 0 0 2
0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 2
generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+3x^34+24x^35+3x^36+1x^38
The gray image is a code over GF(2) with n=136, k=5 and d=68.
This code was found by Heurico 1.16 in 0.0097 seconds.