The generator matrix
1 1 X 1 1 1 1 1
0 X X 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 0 2 0 0 0 0
0 0 0 0 2 0 0 0
0 0 0 0 0 2 0 0
0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 2
generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+12x^2+52x^4+116x^6+512x^7+662x^8+512x^9+116x^10+52x^12+12x^14+1x^16
The gray image is a code over GF(2) with n=32, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00208 seconds.