The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 2 1 0 1 1 1 1 X+2 X X 1 1 X X 1
0 1 1 0 1 1 0 X+1 1 0 X+1 1 2 1 X+1 1 0 1 X+2 3 1 X+2 0 3 1 X X+2 0
0 0 X 0 0 0 0 X X X+2 0 X+2 X 0 2 X X X 2 2 0 X 0 X+2 0 X+2 2 0
0 0 0 X 0 0 0 0 0 0 2 2 X+2 X X X X X+2 2 X X+2 X X+2 0 X+2 X+2 X+2 0
0 0 0 0 X X+2 X+2 X X+2 X 2 2 X 2 X 2 0 X 0 X X 2 X+2 2 0 X+2 X 0
0 0 0 0 0 2 0 0 2 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 0 0
0 0 0 0 0 0 2 2 2 0 2 0 0 2 0 0 0 0 2 2 2 0 0 2 2 0 0 0
generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+76x^20+108x^21+301x^22+510x^23+901x^24+1304x^25+1683x^26+2154x^27+2297x^28+2196x^29+1651x^30+1298x^31+886x^32+544x^33+321x^34+70x^35+63x^36+8x^37+11x^38+1x^54
The gray image is a code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 4.08 seconds.