The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+136x^23+822x^24+1940x^25+4204x^26+5488x^27+7350x^28+5936x^29+4288x^30+1648x^31+673x^32+188x^33+52x^34+24x^35+18x^36

The gray image is a code over GF(2) with n=224, k=15 and d=92.
This code was found by Heurico 1.16 in 3.37 seconds.