The generator matrix

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

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+110x^27+335x^28+628x^29+740x^30+614x^31+654x^32+576x^33+248x^34+98x^35+61x^36+12x^37+4x^38+10x^39+5x^40

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 0.094 seconds.