The generator matrix

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

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+145x^28+104x^30+185x^32+24x^34+43x^36+9x^40+1x^48

The gray image is a code over GF(2) with n=124, k=9 and d=56.
This code was found by Heurico 1.16 in 0.515 seconds.