The generator matrix

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

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+74x^12+16x^13+360x^14+240x^15+683x^16+240x^17+336x^18+16x^19+70x^20+8x^22+4x^24

The gray image is a code over GF(2) with n=128, k=11 and d=48.
This code was found by Heurico 1.16 in 0.015 seconds.