The generator matrix

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

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+72x^48+8x^49+34x^50+48x^51+304x^52+168x^53+382x^54+336x^55+984x^56+696x^57+1356x^58+1216x^59+2008x^60+1296x^61+1924x^62+1024x^63+1591x^64+760x^65+770x^66+400x^67+476x^68+136x^69+126x^70+48x^71+120x^72+8x^73+16x^74+56x^76+16x^80+4x^84

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 13.3 seconds.