The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  1  1  2  1  0  1  1  X  0
 0  1  1  0 X+1  1  X X+3  1  3  1 X+1  0 X+2  2  1  X  1 X+3 X+2  2  0
 0  0  X X+2  0 X+2  X X+2  X  2  0  2  2  0  X X+2  X  2  X  2  X  X
 0  0  0  2  0  0  0  0  0  2  2  0  2  0  0  2  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  2  0  2  0  2  2  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  2  0  0  0  0  2  2  2  2  0  0  2  0  2
 0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  2  0  2  2  0  2  2
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  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+167x^16+32x^17+518x^18+288x^19+1418x^20+704x^21+1918x^22+704x^23+1465x^24+288x^25+498x^26+32x^27+142x^28+10x^30+6x^32+1x^40

The gray image is a code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 15 seconds.