The generator matrix

 1  0  0  1  1  1  0  1  1  1  X  2 X+2  1  1  X  0
 0  1  0  1  X X+3  1  0 X+3  X  1  0  1  3  3  1  1
 0  0  1  1  1  0 X+3  X  X X+1  0  1 X+1 X+1  X  X  0
 0  0  0  X  0 X+2 X+2  X  2  X  X X+2  0  2  X  2  2
 0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  2  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  2  0  2  0  0  2  2  2  0  0

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+52x^11+190x^12+528x^13+1034x^14+1784x^15+2927x^16+3444x^17+2738x^18+1828x^19+1154x^20+504x^21+126x^22+48x^23+16x^24+4x^25+6x^26

The gray image is a code over GF(2) with n=68, k=14 and d=22.
This code was found by Heurico 1.16 in 2.37 seconds.