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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+91x^64+136x^65+196x^66+300x^67+371x^68+432x^69+506x^70+690x^71+893x^72+1098x^73+1343x^74+1432x^75+1444x^76+1514x^77+1301x^78+1092x^79+926x^80+668x^81+548x^82+428x^83+248x^84+196x^85+148x^86+122x^87+113x^88+50x^89+45x^90+32x^91+8x^92+2x^93+5x^94+3x^98+1x^100+1x^114

The gray image is a linear code over GF(2) with n=304, k=14 and d=128.
This code was found by Heurico 1.16 in 25.3 seconds.