The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+145x^28+96x^29+104x^30+320x^31+185x^32+96x^33+24x^34+43x^36+9x^40+1x^48

The gray image is a code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.719 seconds.