The generator matrix

1 1 1 1 1 1 1 X X X X X X X
0 X X 0 X+2 2 2 X X 0 X+2 0 2 X+2
0 0 2 2 2 0 2 0 2 2 0 0 2 2

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+14x^13+40x^14+7x^16+2x^21

The gray image is a code over GF(2) with n=56, k=6 and d=26.
This code was found by an older version of Heurico in 0 seconds.