The generator matrix
1 1 1 1 1 1 1 1 X 1 1
0 2 0 0 0 0 0 0 2 0 0
0 0 2 0 0 0 0 0 2 0 0
0 0 0 2 0 0 0 0 2 0 0
0 0 0 0 2 0 0 0 2 0 0
0 0 0 0 0 2 0 0 2 0 0
0 0 0 0 0 0 2 0 2 0 0
0 0 0 0 0 0 0 2 2 0 0
generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+28x^4+78x^8+128x^10+1536x^11+212x^12+57x^16+8x^20
The gray image is a code over GF(2) with n=88, k=11 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.