The generator matrix

 1  1  1  1  X  1  1 2X  X  1  1
 0  X  0 X+2 3X+2  0 3X+2  X X+2 X+2  X
 0  0  2  0  0  2  2 2X+2 2X 2X+2  0
 0  0  0  2  0  2 2X+2 2X  2  0 2X+2
 0  0  0  0 2X  0  0 2X 2X  0 2X

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+32x^7+95x^8+288x^9+928x^10+1408x^11+935x^12+288x^13+80x^14+32x^15+8x^16+1x^20

The gray image is a code over GF(2) with n=88, k=12 and d=28.
This code was found by Heurico 1.16 in 0.031 seconds.