The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 2 1 X
0 X 0 0 0 X X+2 X 2 2 0 0 X 2 X X+2 X 0 2
0 0 X 0 X X X 0 2 0 X X+2 X+2 2 0 X+2 0 X+2 X
0 0 0 X X 0 X X+2 0 X X 2 2 X+2 X+2 X+2 X 0 0
0 0 0 0 2 0 0 0 2 2 2 0 2 0 2 0 0 2 0
0 0 0 0 0 2 0 2 0 0 2 2 0 2 0 2 2 2 0
generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+90x^14+271x^16+144x^17+386x^18+240x^19+478x^20+112x^21+206x^22+16x^23+80x^24+22x^26+2x^28
The gray image is a code over GF(2) with n=76, k=11 and d=28.
This code was found by Heurico 1.16 in 0.0529 seconds.