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  X  0  1  1  1  1  1
 0  X  0  X 2X  0 3X  X 2X+2 3X+2 2X+2 3X+2  2 2X+2 X+2 3X+2  0 2X  X 3X 2X+2  0 X+2  2 X+2  X 2X  2 2X+2  X 2X
 0  0  X  X 2X+2 3X+2 3X+2 2X+2 2X+2 X+2  X 2X  0 3X+2 3X  2 2X X+2 3X  0 2X 3X 3X+2 2X+2 2X+2 X+2  0 X+2 X+2 2X  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+61x^28+94x^29+188x^30+372x^31+168x^32+62x^33+50x^34+16x^35+10x^36+1x^38+1x^58

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 0.015 seconds.