The generator matrix
1 1 1 1 1 1 1 1 2X+2 1 1
0 2 0 2 0 2X 2 2X+2 2X 0 0
0 0 2X 0 0 2X 2X 2X 0 0 0
0 0 0 2X 2X 2X 2X 0 0 0 0
generates a code of length 11 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+13x^8+56x^10+128x^11+43x^12+8x^14+6x^16+1x^20
The gray image is a code over GF(2) with n=88, k=8 and d=32.
This code was found by Heurico 1.16 in 3.62e-008 seconds.