The generator matrix

 1  0  1  1  1 X+2  X  1  1  2  1  1  1  1  1  1 2X 3X+2  1 3X  1  X  1  1  1  1  X 2X
 0  1 X+1 3X+2  3  1  1 2X 2X+3  1 3X+3 X+2 2X+1 3X X+1 2X+3  1  1  1  1  2  1  X  X 2X+2 X+2  X  X
 0  0 2X+2  0  2 2X+2  2 2X+2 2X  0  2 2X+2 2X  0 2X 2X 2X+2  0 2X+2  0  0  2  2  2 2X+2  2 2X+2 2X+2
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0 2X  0  0 2X 2X 2X  0
 0  0  0  0 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X  0  0 2X  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+133x^24+192x^25+640x^26+512x^27+1053x^28+704x^29+592x^30+128x^31+114x^32+16x^34+7x^36+4x^40

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.078 seconds.