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

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

Homogenous weight enumerator: w(x)=1x^0+64x^72+78x^74+204x^76+512x^77+432x^78+512x^79+124x^80+36x^82+28x^84+16x^86+26x^88+14x^90+1x^144

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 0.64 seconds.