The generator matrix

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

generates a code of length 31 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+196x^26+1148x^27+2046x^28+4132x^29+5347x^30+7184x^31+5201x^32+4340x^33+1846x^34+884x^35+310x^36+100x^37+27x^38+2x^40+4x^41

The gray image is a code over GF(2) with n=248, k=15 and d=104.
This code was found by Heurico 1.16 in 3.94 seconds.