The generator matrix

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

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+176x^7+995x^8+4434x^9+15461x^10+23320x^11+15634x^12+4380x^13+922x^14+200x^15+10x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=88, k=16 and d=28.
This code was found by Heurico 1.16 in 3.14 seconds.