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 2X  0  X  2  X  0  X  0  X  0 2X+2 2X+2  0  1
 0  X  2 3X+2  0 3X+2  2 3X 3X+2  0 3X  2 3X  0 X+2  2 3X  0 3X+2  2 2X 3X 2X+2 3X+2  0 X+2  2 3X 2X 3X+2 2X+2  X 2X 3X+2 2X+2  X 2X X+2 2X+2  X  0  0 3X+2 X+2  2  2 3X 3X  0 2X  0 2X 3X+2 X+2 3X+2 X+2  2  2 2X+2 2X+2 3X 3X  X  X 2X  X 3X+2  X 3X  X 3X+2  X 3X 2X+2  2  0  X  0
 0  0 2X  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X  0  0  0 2X  0  0
 0  0  0 2X  0  0  0  0  0  0  0  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X  0  0  0  0 2X 2X  0 2X  0  0 2X  0 2X  0
 0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X  0  0  0  0 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X  0  0 2X  0 2X  0  0 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X 2X  0  0  0 2X  0  0  0 2X  0  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+7x^72+50x^73+236x^74+110x^75+363x^76+132x^77+372x^78+180x^79+160x^80+114x^81+159x^82+30x^83+109x^84+24x^85+1x^130

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 0.593 seconds.