The generator matrix

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

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+121x^28+248x^30+256x^31+338x^32+8x^34+51x^36+1x^56

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 0.125 seconds.