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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+16x^42+34x^43+95x^44+348x^45+66x^46+368x^47+29x^48+4x^49+45x^50+14x^51+3x^52+1x^90

The gray image is a linear code over GF(2) with n=368, k=10 and d=168.
This code was found by Heurico 1.16 in 0.078 seconds.