The generator matrix

 1  0  0  1  1  1  X  1  1  1  1  2  1  0  X  1 X+2 X+2  X  1  1  1
 0  1  0  1 X+2 X+3  1  2  0 X+1 X+1  1  3  1  X  X  1  0  2 X+3  3  3
 0  0  1  1 X+3 X+2  1  X X+1 X+1  0  X X+1 X+1  1  1 X+1  1  1  2 X+1  3
 0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  2  0  0  0  0
 0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  0  2  2  0  2  0  2  0  2  0
 0  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  0  0  2  0  0  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+64x^16+168x^17+293x^18+706x^19+826x^20+1400x^21+1200x^22+1474x^23+854x^24+728x^25+290x^26+118x^27+46x^28+8x^29+8x^30+6x^31+1x^32+1x^34

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 0.57 seconds.