The generator matrix

 1  0  0  1  1  1  0 X^3+X^2 X^3+X^2 X^3+X^2  1  1  1  1 X^2+X  1  1 X^3+X  1  X  1 X^3+X^2+X  1 X^2+X  1  1 X^3+X  1  1  1 X^2 X^3+X^2  1  1 X^3+X^2+X X^3  1 X^2  1  1 X^3+X  1  1 X^3+X  1  1  1 X^3 X^2  1  X X^3  1 X^2+X  1  1  1  1  X X^3+X X^3+X^2  1 X^3+X^2+X X^3 X^3+X^2+X  1 X^3  1  1  1  1  1  1 X^2 X^3+X^2+X  1
 0  1  0  0 X^2+1 X^3+X^2+1  1  X  1  1 X^2+1 X^2+1 X^3+X^2 X^2 X^2 X^2+X+1 X^2+X  1 X^3+X  1 X^3+X+1 X^3+X^2+X X^3+X^2+X  1 X^3+X X^3+X^2+X+1  1  1  1 X^3+1  1  1 X^2+X  0  X  X X^2+1  1 X^2 X^2+X+1  1 X^2+1  X  1 X^3+X^2+X X^2 X^2+X  1  1  X  1  1 X^3  1 X^2+X+1  0 X^3 X^3+X^2+1  0 X^3+X^2+X  1 X+1  1  1  1 X+1 X^3 X^3+X+1 X^3+1 X^2+X+1 X^3+X^2+1 X^2+X+1  0  1  1  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X X^3+1 X^3+1 X^3+X^2+X  X X^3+X^2+1  1 X^2+X  X X^3+X^2 X^3+X+1 X^2+1  1  1  0 X^2+X+1 X^3+1 X^3+X^2 X^2+X X^3+X^2+1  X X^3+X+1 X^3+X^2+X+1 X^2+X X^2+1 X^3+X  1  1 X^2  1 X^2+1 X^2+X+1 X^3 X^3+X^2+X X^3+X^2+X+1 X^2 X^2+1  X X^2+X X^3  1 X^2 X^2+X X^3 X^3 X^2+1 X^2+X X+1 X^3+X^2+1 X^3+X^2+X+1  1  1  0 X^3+X^2+1 X^3+1 X^3+X^2+X X^3+X  1  1 X^3+X^2+X+1 X^3+X^2+1 X+1 X^3 X^2+X+1 X^3+X+1 X^3+X+1 X^3+1 X^3
 0  0  0 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3 X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3  0 X^2 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2  0 X^3 X^3 X^3 X^3+X^2 X^2  0 X^2 X^2 X^3  0  0  0 X^3 X^3  0 X^3+X^2 X^3  0 X^3+X^2 X^3 X^2 X^2 X^3  0 X^3+X^2  0 X^2 X^3 X^2 X^3 X^3

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+90x^70+852x^71+1103x^72+1566x^73+1782x^74+2166x^75+2046x^76+1966x^77+1547x^78+1218x^79+731x^80+650x^81+288x^82+194x^83+67x^84+70x^85+13x^86+16x^87+1x^88+4x^89+8x^90+1x^92+2x^95+2x^96

The gray image is a linear code over GF(2) with n=608, k=14 and d=280.
This code was found by Heurico 1.16 in 4.98 seconds.