The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+41x^64+54x^65+171x^66+196x^67+432x^68+352x^69+654x^70+480x^71+868x^72+510x^73+890x^74+460x^75+840x^76+464x^77+629x^78+306x^79+317x^80+128x^81+169x^82+70x^83+43x^84+22x^85+34x^86+22x^87+12x^88+4x^89+10x^90+2x^91+4x^92+2x^93+3x^94+1x^96+1x^100

The gray image is a linear code over GF(2) with n=296, k=13 and d=128.
This code was found by Heurico 1.16 in 4.96 seconds.