The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+97x^24+614x^25+1091x^26+1490x^27+1750x^28+1496x^29+916x^30+492x^31+150x^32+58x^33+25x^34+10x^35+2x^36

The gray image is a code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 0.235 seconds.