The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+206x^72+300x^73+444x^74+364x^75+448x^76+388x^77+402x^78+252x^79+267x^80+196x^81+190x^82+116x^83+175x^84+76x^85+78x^86+56x^87+61x^88+32x^89+22x^90+8x^91+9x^92+4x^95+1x^96

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 0.912 seconds.