The generator matrix
1 1 1 1 1 X 1 0 1 1 1
0 X 0 X+2 2 X+2 3X+2 X 2X+2 3X+2 0
0 0 2X+2 0 2 2X 2 2X 0 2X+2 0
0 0 0 2X 2X 2X 2X 0 0 0 0
generates a code of length 11 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+41x^8+42x^9+279x^10+304x^11+278x^12+36x^13+38x^14+2x^17+3x^18
The gray image is a code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.