The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+116x^72+178x^73+175x^74+144x^75+74x^76+60x^77+14x^78+56x^79+51x^80+34x^81+37x^82+40x^83+28x^84+4x^86+8x^88+2x^92+2x^98

The gray image is a code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.11 in 0.23 seconds.