The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+18x^24+56x^25+33x^26+168x^27+476x^28+168x^29+27x^30+56x^31+17x^32+3x^34+1x^54

The gray image is a code over GF(2) with n=224, k=10 and d=96.
This code was found by Heurico 1.16 in 0.031 seconds.