The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+13x^6+25x^8+89x^10+768x^11+91x^12+23x^14+10x^16+3x^18+1x^20

The gray image is a code over GF(2) with n=88, k=10 and d=24.
This code was found by Heurico 1.16 in 0.015 seconds.