The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^7+1073x^8+4578x^9+14847x^10+24152x^11+15086x^12+4492x^13+990x^14+176x^15+2x^17+3x^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 2.99 seconds.