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  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  X  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3
 0  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3
 0  0  0  0 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3
 0  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0  0  0
 0  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+21x^80+40x^82+40x^84+22x^86+128x^87+1550x^88+128x^89+24x^90+32x^92+33x^94+20x^96+8x^98+1x^174

The gray image is a linear code over GF(2) with n=704, k=11 and d=320.
This code was found by Heurico 1.16 in 0.703 seconds.