The generator matrix

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

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+328x^26+410x^27+450x^28+376x^29+168x^30+100x^31+59x^32+16x^33+16x^34+2x^35+2x^36

The gray image is a code over GF(2) with n=224, k=11 and d=100.
This code was found by Heurico 1.16 in 0.031 seconds.