The generator matrix

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

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+43x^16+68x^17+81x^18+130x^19+224x^20+308x^21+332x^22+318x^23+218x^24+156x^25+86x^26+30x^27+24x^28+12x^29+12x^30+2x^31+2x^32+1x^34

The gray image is a code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.069 seconds.