The generator matrix
1 1 1 1 X X X 1 1 1 1
0 X 0 X 0 X X 0 0 2 0
0 0 X X X X 0 0 2 2 0
0 0 0 2 0 0 0 2 2 2 0
0 0 0 0 2 0 0 2 2 0 0
0 0 0 0 0 2 0 2 2 2 2
0 0 0 0 0 0 2 2 0 2 2
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+43x^6+149x^8+192x^9+307x^10+640x^11+339x^12+192x^13+153x^14+22x^16+9x^18+1x^20
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 0.00742 seconds.