The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+307x^28+200x^30+298x^32+152x^34+49x^36+17x^40

The gray image is a code over GF(2) with n=124, k=10 and d=56.
This code was found by Heurico 1.16 in 4.63 seconds.