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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+153x^48+78x^50+8x^51+520x^52+32x^53+496x^54+168x^55+1311x^56+512x^57+1502x^58+848x^59+2178x^60+960x^61+1840x^62+848x^63+1856x^64+512x^65+970x^66+168x^67+809x^68+32x^69+224x^70+8x^71+245x^72+10x^74+73x^76+18x^80+3x^84+1x^92

The gray image is a linear code over GF(2) with n=244, k=14 and d=96.
This code was found by Heurico 1.16 in 21 seconds.