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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+136x^54+16x^55+293x^56+112x^57+302x^58+336x^59+247x^60+560x^61+226x^62+560x^63+241x^64+336x^65+192x^66+112x^67+166x^68+16x^69+128x^70+63x^72+34x^74+11x^76+6x^78+1x^80+1x^96

The gray image is a linear code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 1.23 seconds.