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  X  1  X  1  1  X  X  1  X  X  X
 0 X^3  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0
 0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3

generates a code of length 42 over Z2[X]/(X^4) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+14x^37+40x^38+44x^40+70x^41+768x^42+42x^45+18x^46+17x^48+2x^49+5x^54+2x^56+1x^70

The gray image is a linear code over GF(2) with n=336, k=10 and d=148.
This code was found by Heurico 1.16 in 28.6 seconds.