The generator matrix

 1  1  1  1  1  1  1  1  X  1  1
 0 2X  0  0  0  0  0  0 2X  0  0
 0  0 2X  0  0  0  0  0 2X  0  0
 0  0  0 2X  0  0  0  0 2X  0  0
 0  0  0  0 2X  0  0  0 2X  0  0
 0  0  0  0  0 2X  0  0 2X  0  0
 0  0  0  0  0  0 2X  0 2X  0  0
 0  0  0  0  0  0  0 2X 2X  0  0

generates a code of length 11 over Z4[X]/(X^2+2) 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 -6.48e-008 seconds.