The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+198x^29+318x^30+168x^31+125x^32+108x^33+64x^34+24x^35+14x^37+2x^38+2x^40

The gray image is a code over GF(2) with n=248, k=10 and d=116.
This code was found by Heurico 1.16 in 47.7 seconds.