The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+228x^27+324x^28+600x^29+432x^30+978x^31+559x^32+512x^33+128x^34+194x^35+76x^36+40x^37+16x^38+6x^39+2x^43

The gray image is a code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 29.2 seconds.