The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+85x^28+68x^29+268x^30+252x^31+201x^32+60x^33+44x^34+4x^35+40x^36+1x^52

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 0.031 seconds.