The generator matrix

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

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+221x^72+249x^74+213x^76+145x^78+103x^80+51x^82+30x^84+3x^86+2x^88+4x^100+1x^104+1x^108

The gray image is a code over GF(2) with n=304, k=10 and d=144.
This code was found by Heurico 1.16 in 84.6 seconds.