The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+120x^25+958x^26+676x^27+937x^28+412x^29+640x^30+188x^31+125x^32+12x^33+26x^34+1x^36

The gray image is a code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.16 in 0.063 seconds.