The generator matrix

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

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+129x^28+452x^29+276x^30+384x^31+246x^32+440x^33+90x^34+7x^36+4x^37+16x^38+1x^40+2x^42

The gray image is a code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 0.031 seconds.