The generator matrix
1 1 1 1 1 1 1 1 1 X X 1 1
0 2 0 0 0 0 0 0 2 0 2 2 0
0 0 2 0 0 0 0 0 2 2 2 0 0
0 0 0 2 0 0 0 2 0 2 0 2 0
0 0 0 0 2 0 0 2 0 0 2 2 0
0 0 0 0 0 2 0 2 2 0 0 2 0
0 0 0 0 0 0 2 2 2 2 2 2 0
generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+26x^8+12x^10+32x^11+24x^12+832x^13+28x^14+32x^15+13x^16+20x^18+4x^22
The gray image is a code over GF(2) with n=104, k=10 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.