The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X+2 2 1 2 X+2 1 X 1 1 X 1 1
0 1 1 0 1 1 0 X+1 1 0 3 1 1 2 1 1 1 X+2 0 X+2 0 X+1 X+3
0 0 X 0 0 0 0 X X X+2 2 X X+2 2 X X+2 0 X X+2 X 2 X 0
0 0 0 X 0 0 0 0 0 0 0 0 2 X X X+2 X 2 X 2 2 X+2 X
0 0 0 0 X X+2 X+2 X X+2 X 2 X 0 X X 0 2 X+2 0 X X+2 2 0
0 0 0 0 0 2 0 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 2
0 0 0 0 0 0 2 2 2 0 0 0 2 2 2 2 0 0 0 2 0 0 2
generates a code of length 23 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+114x^16+24x^17+619x^18+376x^19+1570x^20+1488x^21+2759x^22+2352x^23+2908x^24+1528x^25+1588x^26+344x^27+564x^28+32x^29+88x^30+25x^32+1x^34+2x^36+1x^38
The gray image is a code over GF(2) with n=92, k=14 and d=32.
This code was found by Heurico 1.16 in 2.97 seconds.