The generator matrix

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

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+220x^27+647x^28+1198x^29+1102x^30+1856x^31+1387x^32+988x^33+443x^34+208x^35+61x^36+62x^37+6x^38+12x^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 0.25 seconds.