The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1 X+2  1  1 X+2  1  1  2  1  1  2  1  1  2  1  1  2  0  1  1  1 X+2  1  2  1  1  X  1  1  0 X+2 X+2  1 X+2  1  1  1  1  X X+2  0  X  0  2  X  X  0 X+2  0  2  0  0  0  1  0 X+2  X  1  1  0  1  1 X+2  0
 0  1  1 X+2 X+3  1  1 X+1  X  3  1  2  X X+1  1  X X+1  1  0  1  1  0  1  1  0 X+3  1 X+2  1  1  1  2 X+3  X  1  3  1 X+3  1  1 X+1 X+1  X  1  1  2  1  2 X+2 X+2  3  0  1  1  1  1  1  1  1  1  1  1  2  1  1  1 X+2  1  1  1 X+3 X+2  1 X+3  0  1  1
 0  0  X  0 X+2  X  X  2  X  2  0  X X+2  2  0  0  X X+2  0 X+2  0 X+2  2 X+2  0  X  X  0  X X+2  0 X+2  2 X+2  0  2  0  X  X  X  2  0  2  2 X+2 X+2  2  2 X+2  2  0 X+2  X X+2  2  0  2  X X+2 X+2 X+2  X  X  X X+2  0  X  2  2  0  0 X+2  X  X  2 X+2  2
 0  0  0  2  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  0  2  2  0  0  0  2  0  2  2  2  0  2  0  2  2  2  0  0  0  2  2  0  0  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  2  2  0  0  0  0  0  0  2  0
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  0  0  2  0  2  2  2  2  2  0  2  2  0  0  0  2  0  2  2  2  2  2  2  2  2  2

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+34x^72+96x^73+143x^74+118x^75+133x^76+156x^77+68x^78+50x^79+57x^80+52x^81+35x^82+20x^83+25x^84+12x^85+4x^86+2x^87+6x^88+4x^89+4x^90+2x^91+2x^110

The gray image is a code over GF(2) with n=308, k=10 and d=144.
This code was found by Heurico 1.16 in 0.358 seconds.