The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1  1  1  X  1 X^2+2  1  0  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+1  1 X^2+X X^2+1  1  0 X+2 X^2+1 X^2+X+3  0  3  1 X^2+2  X  2
 0  0  2  0  0  2  2  0  0  2  2  2  0  0  2  0  2  0  2  0  0  2  2  0  2  2  2  2
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  0  0  2  2  2  0  0  2  0  2
 0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  0  0  2  2  2  2  0  0  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+17x^24+168x^25+241x^26+376x^27+447x^28+392x^29+234x^30+136x^31+14x^32+16x^33+3x^34+1x^36+1x^38+1x^46

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 0.032 seconds.