The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X X^2  0  1  X X^2  X  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2  2 X^2+2  0 X^2+2  0 X^2+2 X^2  0  2 X^2  0 X^2+2 X^2+2  2  2 X^2+2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 X^2+2  0
 0  0  2  0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0  2  0  2  2  2
 0  0  0  2  0  0  0  2  0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  2  0  2  2  0  2  2  2
 0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  2  2  0  2  2  2  0  0  2  0  0  0  2  2
 0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  2  0  0  2  0  2  0  0  2  0  2  0  2  2  0  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  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+81x^26+16x^27+118x^28+192x^29+450x^30+352x^31+450x^32+192x^33+96x^34+16x^35+66x^36+6x^38+4x^40+7x^42+1x^48

The gray image is a code over GF(2) with n=248, k=11 and d=104.
This code was found by Heurico 1.16 in 69.7 seconds.