The generator matrix

 1  0  1  1 2X+2  1  2  1  1  1  1  0  1  1 2X+2  1  1 2X+2 3X  1  1 3X+2 3X+2  1 3X+2  1 3X 2X  1  1 3X
 0  1  1 3X+2  1 3X+3  1 2X+2 X+1  X 2X+3  1  0 X+1  1 3X+2 2X+3  1  1 X+3 X+3  1  1 X+2  1 2X+2  1  X  X 2X  1
 0  0  X  0 3X  X X+2 3X 2X 3X 2X  2  2 2X+2 2X+2  2 2X+2 3X 3X+2  0 X+2 2X 3X X+2  0 2X+2 2X+2 X+2 3X 3X+2 2X
 0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X 2X 2X 2X  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+474x^28+408x^29+912x^30+616x^31+882x^32+360x^33+336x^34+24x^35+61x^36+16x^38+5x^40+1x^44

The gray image is a code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 27.9 seconds.