The generator matrix
1 0 1 1 1 0 X 1 1 1 1
0 1 1 0 X+1 1 X 0 X+2 0 0
0 0 X X+2 0 X+2 X 0 2 0 0
0 0 0 2 0 0 2 0 0 2 0
0 0 0 0 2 0 2 2 2 2 0
0 0 0 0 0 2 2 2 0 0 0
generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+44x^6+142x^8+192x^9+320x^10+640x^11+336x^12+192x^13+140x^14+33x^16+8x^18
The gray image is a code over GF(2) with n=44, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00644 seconds.