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  X  X  X  0 X^2  0  1  1  1  1  X  X  X  X  1  X  0  X  1  1  X  1  1  1 X^2  X  0  1  1  0  1  1  1  X  1  1
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X X^2  0 X^2+X X^2+X X^2 X^2 X^2+X  X  X  X  X  0 X^2 X^2+X  X X^2 X^2  X  X X^2 X^2  0  0 X^2+X X^2+X  X  X X^2+X X^2+X  X  X  X X^2+X X^2+X X^2+X  X X^2  0  0 X^2 X^2+X  0  X  0  0 X^2 X^2  0  0
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X  0  X X^2  X  0 X^2  X  0  X X^2 X^2+X X^2+X  0 X^2+X  0  X  X  X  X  0 X^2  X X^2 X^2 X^2 X^2  X X^2+X  0 X^2+X X^2 X^2 X^2+X  X  0 X^2  0  0  X X^2+X  X  0 X^2+X  X  0  0  X  X  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  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+51x^48+170x^50+369x^52+72x^53+606x^54+216x^55+1212x^56+432x^57+1606x^58+816x^59+1995x^60+1024x^61+2353x^62+800x^63+1768x^64+464x^65+981x^66+208x^67+544x^68+56x^69+360x^70+8x^71+162x^72+56x^74+31x^76+9x^78+6x^80+3x^82+5x^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 18.8 seconds.