The generator matrix

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

generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+18x^44+34x^45+26x^46+48x^47+12x^48+52x^49+4x^50+32x^51+26x^53+1x^56+1x^58+1x^66

The gray image is a linear code over GF(2) with n=192, k=8 and d=88.
This code was found by Heurico 1.16 in 0.0521 seconds.