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

generates a code of length 48 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+72x^40+92x^41+140x^42+204x^43+236x^44+312x^45+377x^46+434x^47+426x^48+434x^49+358x^50+316x^51+241x^52+134x^53+116x^54+68x^55+41x^56+50x^57+25x^58+7x^60+2x^61+6x^62+2x^63+1x^66+1x^70

The gray image is a linear code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 0.836 seconds.