The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+76x^16+176x^18+256x^19+508x^20+768x^21+544x^22+768x^23+488x^24+256x^25+176x^26+68x^28+11x^32

The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.167 seconds.