The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  1  1  1  1  X  2  1  1  1  2  X  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2 X+2  2  X X^2+X+2 X^2+2 X^2+X+2  X X^2+X+2 X^2 X^2+X  X X+2 X+2  0 X^2 X^2+X+2  2
 0  0 X^2+2  0 X^2 X^2  2 X^2  0  2  0  0 X^2  2 X^2 X^2 X^2+2 X^2  0 X^2  0 X^2+2  2  2  2 X^2 X^2+2 X^2
 0  0  0  2  0  0  2  0  0  2  2  0  0  0  2  0  2  2  0  2  2  2  2  0  2  0  0  0
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  2  0  0  2  0  0  0  0  0  2  0  0  0  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+99x^24+136x^25+178x^26+432x^27+376x^28+464x^29+134x^30+112x^31+88x^32+8x^33+6x^34+11x^36+2x^38+1x^44

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 0.062 seconds.