The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X^2 X^2 0
0 X 0 X^2+X X^2 X^2+X+2 X^2+2 X 0 X^2+X X^2 X X^2 X+2 2 X^2+X 0 X^2+X+2 X^2+X+2 X^2 X^2 X
0 0 X^2+2 0 X^2 X^2 2 X^2 2 2 X^2+2 X^2 0 2 X^2+2 2 0 X^2+2 2 X^2 X^2+2 0
0 0 0 2 2 0 2 2 0 2 0 0 2 0 2 0 2 2 0 2 0 0
generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 19.
Homogenous weight enumerator: w(x)=1x^0+80x^19+113x^20+212x^21+244x^22+204x^23+73x^24+76x^25+4x^26+4x^27+12x^28+1x^36
The gray image is a code over GF(2) with n=176, k=10 and d=76.
This code was found by Heurico 1.16 in 0.094 seconds.