The generator matrix

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

generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+46x^10+32x^11+46x^12+2x^14+1x^16

The gray image is a code over GF(2) with n=88, k=7 and d=40.
This code was found by Heurico 1.16 in 0 seconds.