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

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+35x^74+50x^76+16x^77+36x^78+64x^79+288x^80+1120x^81+282x^82+64x^83+15x^84+16x^85+11x^86+16x^88+11x^90+4x^92+8x^94+7x^96+3x^100+1x^150

The gray image is a linear code over GF(2) with n=648, k=11 and d=296.
This code was found by Heurico 1.16 in 31.9 seconds.