The generator matrix

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

generates a code of length 16 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+207x^12+1168x^13+2807x^14+7452x^15+9361x^16+7752x^17+2742x^18+992x^19+239x^20+40x^21+3x^22+4x^23

The gray image is a linear code over GF(2) with n=128, k=15 and d=48.
This code was found by Heurico 1.16 in 2.23 seconds.