The generator matrix

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

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+476x^26+1988x^27+4361x^28+7738x^29+11760x^30+12478x^31+12402x^32+8054x^33+3956x^34+1576x^35+545x^36+158x^37+32x^38+6x^39+1x^40+2x^41+2x^44

The gray image is a code over GF(2) with n=248, k=16 and d=104.
This code was found by Heurico 1.16 in 15.4 seconds.