The generator matrix

 1  0  0  1  1  1 2X  X  1  1  1  2  1  X  1 2X 3X+2  1 X+2  1  1  1  1  1  1  X  1  1  1  1  1
 0  1  0  0  3  1  1  X  3 2X+1  2  1 3X  1 3X+1 3X  1 X+2  1 3X+3 2X X+2 3X+1 2X+2 3X+3  0  3  1 2X+3 X+3 2X
 0  0  1 X+1 3X+3 2X+2 3X+3  1  3 3X 3X+2 3X+2 X+1 3X+3 X+3  1  0  X 2X+1  X  3  1 2X+2 3X+3 X+3  1 3X+2 2X+1 3X+1 3X+1 2X+2
 0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X  0 2X  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+116x^27+697x^28+1054x^29+1533x^30+1724x^31+1265x^32+904x^33+647x^34+136x^35+61x^36+26x^37+19x^38+8x^39+1x^42

The gray image is a code over GF(2) with n=248, k=13 and d=108.
This code was found by Heurico 1.16 in 0.281 seconds.