The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 2 1 X 1 1 1 0 1 0 0 X
0 X 0 X 0 0 X X+2 2 2 X X+2 0 2 X X+2 X X+2 X+2 X X X 0 0 0 2 0
0 0 X X 0 X+2 X 2 0 X X X+2 2 X+2 0 2 X+2 2 0 X 2 X+2 X 0 X X 0
0 0 0 2 0 0 2 0 0 0 0 0 2 2 0 0 2 2 2 2 2 0 2 2 0 2 0
0 0 0 0 2 0 0 0 2 2 0 2 2 2 0 2 0 0 0 2 2 0 0 2 2 2 2
0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 0 2 2 0 2 2 2 2 2 2 0 2
generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+64x^22+8x^23+134x^24+64x^25+203x^26+112x^27+197x^28+64x^29+91x^30+8x^31+44x^32+25x^34+7x^36+1x^38+1x^40
The gray image is a code over GF(2) with n=108, k=10 and d=44.
This code was found by Heurico 1.16 in 0.0323 seconds.