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

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+61x^72+119x^74+80x^75+242x^76+304x^77+490x^78+304x^79+208x^80+80x^81+68x^82+55x^84+22x^86+6x^88+5x^90+2x^92+1x^140

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 0.625 seconds.