The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+126x^66+120x^67+168x^68+232x^69+159x^70+188x^71+194x^72+180x^73+123x^74+176x^75+110x^76+80x^77+89x^78+28x^79+20x^80+20x^81+11x^82+12x^84+4x^86+5x^88+1x^92+1x^100

The gray image is a code over GF(2) with n=288, k=11 and d=132.
This code was found by Heurico 1.16 in 0.466 seconds.