The generator matrix

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

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+122x^26+638x^27+1186x^28+2028x^29+2752x^30+3186x^31+2575x^32+1968x^33+1092x^34+554x^35+186x^36+68x^37+16x^38+6x^39+4x^40+2x^42

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 1.02 seconds.