The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  1  X  X  2  X  1  2  1  X  1  2  1  1  1  X  2  1  2  2  1  X  X  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  0  2  0  0  0  2  2  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  2  2  0  0  2  2  0  0  0  2  2  2  2  2  0  2  0  2
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  2  0  2  2  0  2  2  0  2  2  2  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  0  2  2  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  2  0  2  2  2  0  2  2  2  0  0  2  0  0  2  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  2  2  0  2  0  2  0  2  2  2  2  0  0  2  2  0  0  0  2  0  2  0  0  0  0  2  2  0  2  2  2  2  2  0  0  0  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  0  2  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  0  0  0  2  0  0  2  2  2  0  2  2  0  0  0  2  2  0  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  0  2  2  2  2  2  0  0  0  0  2  2  2  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  0  0  0  2  2  2  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  0  0  2  2  0  2  2  2  2  0  0  0  2  2  2  2  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  2  2  2  2  2  0  2  0  2  2  0  0  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  0  2  0  0  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  0  0  2  0  0  0  0  2  0  2  2  2  2  0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  2  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  2  0  2  2  2  2  2  0  2  0  0  2  0  2  0  0  2  2  0  0  2  2  2  0  0

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+54x^66+107x^68+149x^70+208x^72+290x^74+64x^75+372x^76+384x^77+423x^78+960x^79+499x^80+1280x^81+488x^82+960x^83+400x^84+384x^85+340x^86+64x^87+267x^88+161x^90+109x^92+91x^94+58x^96+44x^98+19x^100+5x^102+6x^104+3x^106+1x^108+1x^120

The gray image is a code over GF(2) with n=324, k=13 and d=132.
This code was found by Heurico 1.16 in 10.4 seconds.