The generator matrix
1 0 1 1 1 0 1 1 0 X 0
0 1 1 0 X+1 1 0 X+1 1 2 X
0 0 X 0 X 0 X 0 X 0 2
0 0 0 X X X+2 X 0 X X 0
0 0 0 0 2 0 0 0 2 2 2
0 0 0 0 0 2 0 2 0 2 0
0 0 0 0 0 0 2 2 2 2 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+101x^6+80x^7+489x^8+768x^9+1953x^10+1376x^11+1995x^12+768x^13+495x^14+80x^15+74x^16+11x^18+1x^20
The gray image is a code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 0.216 seconds.