The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+104x^72+322x^73+635x^74+806x^75+1108x^76+1084x^77+1196x^78+1116x^79+1445x^80+1172x^81+1282x^82+1204x^83+1257x^84+912x^85+848x^86+584x^87+511x^88+288x^89+229x^90+118x^91+45x^92+58x^93+32x^94+12x^95+3x^96+2x^97+2x^98+6x^100+2x^101

The gray image is a code over GF(2) with n=324, k=14 and d=144.
This code was found by Heurico 1.16 in 15.2 seconds.