The generator matrix

 1  0  0  1  1  1  2  0  1  1  X  1  1  X  1  0  1  1  1  1  1  1
 0  1  0  0  1  1  1  X  2  3  1  X X+3  1  0  X  3  3 X+2 X+2  0  2
 0  0  1  1  2  3  1  1  X X+2  1 X+1  3  0 X+1  1  1 X+3  1 X+2 X+1  1
 0  0  0  2  0  2  2  2  2  2  0  0  0  2  2  0  0  2  2  0  0  0

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+144x^19+134x^20+204x^21+150x^22+164x^23+69x^24+84x^25+16x^26+44x^27+12x^28+2x^30

The gray image is a code over GF(2) with n=88, k=10 and d=38.
This code was found by Heurico 1.11 in 2.05 seconds.