The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  1  1  X  1  2  1  0  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  0 3X 2X+3 X+3  0 2X+1  1  2  X 2X
 0  0 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X 2X 2X
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0  0 2X 2X 2X  0  0 2X  0 2X
 0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0  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+17x^24+168x^25+241x^26+376x^27+447x^28+392x^29+234x^30+136x^31+14x^32+16x^33+3x^34+1x^36+1x^38+1x^46

The gray image is a code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.031 seconds.