The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 2 1 1 X 1 0 1 0
0 X 0 X 0 0 X X+2 2 2 X X+2 X+2 X+2 2 2 0 X+2 0 X+2 X X+2 0 X 0 2 0 X
0 0 X X 0 X+2 X 2 0 X X 0 2 X 2 X+2 X+2 X+2 X 0 X+2 X X X X+2 X X+2 0
0 0 0 2 0 0 2 0 0 0 0 2 2 0 2 2 2 2 2 0 2 0 2 2 0 0 2 2
0 0 0 0 2 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 0 0 0 2 2 0 0 0
0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 2 0 0 2 0 2 0 2 0 0 2 2
generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+168x^24+64x^25+192x^27+193x^28+192x^29+64x^31+127x^32+22x^36+1x^44
The gray image is a code over GF(2) with n=112, k=10 and d=48.
This code was found by Heurico 1.16 in 4.22 seconds.