The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+52x^14+32x^15+142x^16+184x^17+294x^18+616x^19+868x^20+1192x^21+1348x^22+1240x^23+916x^24+648x^25+312x^26+152x^27+108x^28+24x^29+40x^30+8x^31+13x^32+2x^34

The gray image is a code over GF(2) with n=88, k=13 and d=28.
This code was found by Heurico 1.16 in 0.764 seconds.