The generator matrix

 1  0  0  1  1  1  X  1  1  1  2  0  2  1 X+2  1  1  0  2  0  1  1
 0  1  0  X  1 X+3  1 X+2  X X+1  1  1  X X+3  1 X+3  1 X+2  1  0  0 X+2
 0  0  1  1 X+3 X+2  1 X+3  X X+1  X X+1  1  X X+1  3  X  1  1  1 X+1  0
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  2  2  0  2
 0  0  0  0  2  0  0  0  0  2  2  2  2  0  0  0  2  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  0  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+205x^16+160x^17+858x^18+928x^19+2271x^20+1984x^21+3546x^22+1984x^23+2336x^24+928x^25+830x^26+160x^27+168x^28+14x^30+10x^32+1x^36

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 28.3 seconds.