The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+252x^26+128x^27+359x^28+32x^29+188x^30+32x^31+22x^32+8x^34+1x^36+1x^40

The gray image is a code over GF(2) with n=224, k=10 and d=104.
This code was found by Heurico 1.16 in 0.032 seconds.