The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 X X 1 X 1 X 1 1 1 1 1 1 0 2 X 1 1 1 1
0 X 0 0 0 0 0 2 2 X X+2 X X X X+2 X 0 X+2 2 X X X 0 X X+2 X X 2 X+2 2 X+2 X+2 0 X X 2 2 0 0 X
0 0 X 0 0 2 X+2 X X X X X X+2 0 0 0 2 2 X+2 X 0 0 X+2 2 0 X+2 X 2 X 2 X X 2 X X 0 2 X+2 X+2 2
0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 0 X X 2 X 2 X+2 0 2 X+2 2 X+2 0 2 2 X+2 X 0 X+2 2 X+2 X+2 X X+2 X 0 0 0
0 0 0 0 X X 2 X+2 X X+2 2 2 X 2 X+2 X X 2 2 X+2 X+2 2 2 X+2 2 2 0 X+2 2 2 X X+2 0 0 X 0 X 0 2 X+2
generates a code of length 40 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+110x^34+16x^35+182x^36+144x^37+188x^38+352x^39+176x^40+352x^41+102x^42+144x^43+94x^44+16x^45+96x^46+58x^48+16x^50+1x^64
The gray image is a code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.181 seconds.