The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  1  1  0 X^2+X  1  1  1  1  0 X^2+X  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X^2+X X+1 X^2+1  1  1  0 X^2+X X+1 X^2+1  1  1  2 X^2+2 X^2+X+2  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  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+68x^25+120x^26+284x^27+76x^28+284x^29+120x^30+68x^31+1x^32+2x^40

The gray image is a code over GF(2) with n=224, k=10 and d=100.
This code was found by Heurico 1.16 in 0.015 seconds.