The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+56x^66+130x^67+217x^68+390x^69+462x^70+558x^71+687x^72+724x^73+659x^74+674x^75+759x^76+580x^77+543x^78+544x^79+417x^80+282x^81+159x^82+126x^83+66x^84+52x^85+26x^86+10x^87+23x^88+18x^89+11x^90+6x^91+5x^92+2x^93+1x^94+3x^98+1x^100

The gray image is a code over GF(2) with n=300, k=13 and d=132.
This code was found by Heurico 1.16 in 5.24 seconds.