The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+26x^7+60x^8+90x^9+202x^10+1300x^11+188x^12+100x^13+52x^14+18x^15+7x^16+2x^17+2x^18

The gray image is a code over GF(2) with n=88, k=11 and d=28.
This code was found by Heurico 1.16 in 0.016 seconds.