The generator matrix

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

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+89x^6+920x^7+4160x^8+17412x^9+56159x^10+104592x^11+56204x^12+17544x^13+4103x^14+824x^15+115x^16+20x^17+1x^18

The gray image is a code over GF(2) with n=88, k=18 and d=24.
This code was found by Heurico 1.16 in 32.1 seconds.