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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+57x^72+97x^74+213x^76+256x^77+847x^78+256x^79+192x^80+49x^82+38x^84+29x^86+10x^88+2x^90+1x^148

The gray image is a code over GF(2) with n=624, k=11 and d=288.
This code was found by Heurico 1.16 in 0.609 seconds.